﻿<?xml version="1.0" encoding="utf-8"?>
<InstanceReport xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:xsd="http://www.w3.org/2001/XMLSchema">
  <Version>2.2.0.7</Version>
  <hasSegments>false</hasSegments>
  <ReportName>Financing Arrangements</ReportName>
  <ReportLongName>0207 - Disclosure - Financing Arrangements</ReportLongName>
  <DisplayLabelColumn>true</DisplayLabelColumn>
  <ShowElementNames>false</ShowElementNames>
  <RoundingOption />
  <HasEmbeddedReports>false</HasEmbeddedReports>
  <Columns>
    <Column>
      <LabelColumn>false</LabelColumn>
      <Id>1</Id>
      <Labels>
        <Label Id="1" Label="3 Months Ended" />
        <Label Id="2" Label="Sep. 30, 2010" />
      </Labels>
      <CurrencyCode>USD</CurrencyCode>
      <FootnoteIndexer />
      <hasSegments>false</hasSegments>
      <hasScenarios>false</hasScenarios>
      <Segments />
      <Scenarios />
      <Units>
        <Unit>
          <UnitID>USD</UnitID>
          <UnitType>Standard</UnitType>
          <StandardMeasure>
            <MeasureSchema>http://www.xbrl.org/2003/iso4217</MeasureSchema>
            <MeasureValue>USD</MeasureValue>
            <MeasureNamespace>iso4217</MeasureNamespace>
          </StandardMeasure>
          <Scale>0</Scale>
        </Unit>
        <Unit>
          <UnitID>USDEPS</UnitID>
          <UnitType>Divide</UnitType>
          <NumeratorMeasure>
            <MeasureSchema>http://www.xbrl.org/2003/iso4217</MeasureSchema>
            <MeasureValue>USD</MeasureValue>
            <MeasureNamespace>iso4217</MeasureNamespace>
          </NumeratorMeasure>
          <DenominatorMeasure>
            <MeasureSchema>http://www.xbrl.org/2003/instance</MeasureSchema>
            <MeasureValue>shares</MeasureValue>
            <MeasureNamespace>xbrli</MeasureNamespace>
          </DenominatorMeasure>
          <Scale>0</Scale>
        </Unit>
        <Unit>
          <UnitID>Shares</UnitID>
          <UnitType>Standard</UnitType>
          <StandardMeasure>
            <MeasureSchema>http://www.xbrl.org/2003/instance</MeasureSchema>
            <MeasureValue>shares</MeasureValue>
            <MeasureNamespace>xbrli</MeasureNamespace>
          </StandardMeasure>
          <Scale>0</Scale>
        </Unit>
      </Units>
      <CurrencySymbol>$</CurrencySymbol>
    </Column>
  </Columns>
  <Rows>
    <Row>
      <Id>2</Id>
      <Label>Financing Arrangements [Abstract]</Label>
      <Level>0</Level>
      <ElementName>us-gaap_ShortTermBorrowingsAbstract</ElementName>
      <ElementPrefix>us-gaap</ElementPrefix>
      <IsBaseElement>true</IsBaseElement>
      <BalanceType>na</BalanceType>
      <PeriodType>duration</PeriodType>
      <ShortDefinition>No definition available.</ShortDefinition>
      <IsReportTitle>false</IsReportTitle>
      <IsSegmentTitle>false</IsSegmentTitle>
      <IsSubReportEnd>false</IsSubReportEnd>
      <IsCalendarTitle>false</IsCalendarTitle>
      <IsTuple>false</IsTuple>
      <IsAbstractGroupTitle>true</IsAbstractGroupTitle>
      <IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow>
      <IsEquityAdjustmentRow>false</IsEquityAdjustmentRow>
      <IsBeginningBalance>false</IsBeginningBalance>
      <IsEndingBalance>false</IsEndingBalance>
      <IsReverseSign>false</IsReverseSign>
      <PreferredLabelRole />
      <IsEPS>false</IsEPS>
      <FootnoteIndexer />
      <Cells>
        <Cell>
          <Id>1</Id>
          <ShowCurrencySymbol>false</ShowCurrencySymbol>
          <IsNumeric>false</IsNumeric>
          <IsRatio>false</IsRatio>
          <DisplayZeroAsNone>false</DisplayZeroAsNone>
          <NumericAmount>0</NumericAmount>
          <RoundedNumericAmount>0</RoundedNumericAmount>
          <NonNumbericText />
          <NonNumericTextHeader />
          <FootnoteIndexer />
          <hasSegments>false</hasSegments>
          <hasScenarios>false</hasScenarios>
          <DisplayDateInUSFormat>false</DisplayDateInUSFormat>
        </Cell>
      </Cells>
      <OriginalInstanceReportColumns />
      <ElementDataType>xbrli:stringItemType</ElementDataType>
      <SimpleDataType>string</SimpleDataType>
      <ElementDefenition>No definition available.</ElementDefenition>
      <IsTotalLabel>false</IsTotalLabel>
    </Row>
    <Row>
      <Id>3</Id>
      <Label>Financing Arrangements</Label>
      <Level>1</Level>
      <ElementName>us-gaap_ShortTermDebtTextBlock</ElementName>
      <ElementPrefix>us-gaap</ElementPrefix>
      <IsBaseElement>true</IsBaseElement>
      <BalanceType>na</BalanceType>
      <PeriodType>duration</PeriodType>
      <ShortDefinition>No definition available.</ShortDefinition>
      <IsReportTitle>false</IsReportTitle>
      <IsSegmentTitle>false</IsSegmentTitle>
      <IsSubReportEnd>false</IsSubReportEnd>
      <IsCalendarTitle>false</IsCalendarTitle>
      <IsTuple>false</IsTuple>
      <IsAbstractGroupTitle>false</IsAbstractGroupTitle>
      <IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow>
      <IsEquityAdjustmentRow>false</IsEquityAdjustmentRow>
      <IsBeginningBalance>false</IsBeginningBalance>
      <IsEndingBalance>false</IsEndingBalance>
      <IsReverseSign>false</IsReverseSign>
      <PreferredLabelRole>verboselabel</PreferredLabelRole>
      <IsEPS>false</IsEPS>
      <FootnoteIndexer />
      <Cells>
        <Cell>
          <Id>1</Id>
          <ShowCurrencySymbol>false</ShowCurrencySymbol>
          <IsNumeric>false</IsNumeric>
          <IsRatio>false</IsRatio>
          <DisplayZeroAsNone>false</DisplayZeroAsNone>
          <NumericAmount>0</NumericAmount>
          <RoundedNumericAmount>0</RoundedNumericAmount>
          <NonNumbericText>&lt;!--DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd" --&gt;
   &lt;!-- Begin Block Tagged Note 7 - us-gaap:ShortTermDebtTextBlock--&gt;
   &lt;div style="font-family: 'Times New Roman',Times,serif"&gt;
   &lt;div align="left" style="font-size: 10pt; margin-top: 12pt"&gt;&lt;font style="font-variant: small-caps"&gt;&lt;b&gt;Note 7: Financing Arrangements&lt;/b&gt;&lt;/font&gt;
   &lt;/div&gt;
   &lt;div align="left" style="font-size: 10pt; margin-top: 6pt"&gt;Dionex has unsecured credit agreements with domestic and international financial institutions. The
   agreements provide for revolving unsecured lines of credit that we utilize primarily for our
   general corporate purposes, including stock repurchases and working capital needs. As of September
   30, 2010, we had a total of $29.2&amp;#160;million in available lines of credit, maturing on December&amp;#160;31,
   2010 at an annual interest rate of 1.9%, under which we had borrowed $17.4&amp;#160;million.
   &lt;/div&gt;
   &lt;div align="left" style="font-size: 10pt; margin-top: 6pt"&gt;One of our foreign subsidiaries transfers certain customer receivables to financial institutions at
   a discount up to approximately 2% (&amp;#8220;discounted notes&amp;#8221;) and accounts for these transfers as sales.
   The purpose of these transfers is to facilitate the funding of outstanding customer receivables by
   the Company. In the unlikely event that there is failure by the customers to repay the financial
   institutions for the discounted notes sold by Dionex, Dionex would be required to repurchase the
   discounted notes back, up to the specified amount outstanding. Under no other circumstance is
   Dionex obligated or do we have a right to repurchase these discounted notes. Dionex has determined that
   the fair value of these contingent liabilities under these arrangements are not material as of
   September&amp;#160;30, 2010 based on past experience of transferring discounted notes, which considers
   customers&amp;#8217; credit quality, historical loss experience, and whether the repurchase (if required in
   the event of a default) is probable and reasonably estimable. The length of time that these
   discounted notes are outstanding is approximately 90&amp;#160;days and during the three-months ended
   September&amp;#160;30, 2010, Dionex recorded no losses as a result of customers&amp;#8217; failures to repay the
   financial institutions. Total discounted notes transferred to the financial institutions during the
   three months ended September&amp;#160;30, 2010 was $1.2&amp;#160;million and outstanding discounted notes sold as of
   September&amp;#160;30, 2010 was approximately $1.2&amp;#160;million.
   &lt;/div&gt;
   &lt;/div&gt;
</NonNumbericText>
          <NonNumericTextHeader>&lt;!--DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd" --&gt;
   &lt;!-- Begin Block Tagged Note</NonNumericTextHeader>
          <FootnoteIndexer />
          <hasSegments>false</hasSegments>
          <hasScenarios>false</hasScenarios>
          <DisplayDateInUSFormat>false</DisplayDateInUSFormat>
        </Cell>
      </Cells>
      <OriginalInstanceReportColumns />
      <ElementDataType>us-types:textBlockItemType</ElementDataType>
      <SimpleDataType>textblock</SimpleDataType>
      <ElementDefenition>This element may be used as a single block of text to encapsulate the entire disclosure for short-term borrowings including data and tables.</ElementDefenition>
      <ElementReferences>Reference 1: http://www.xbrl.org/2003/role/presentationRef
 -Publisher SEC
 -Name Regulation S-X (SX)
 -Number 210
 -Section 03
 -Paragraph 16
 -Article 7

Reference 2: http://www.xbrl.org/2003/role/presentationRef
 -Publisher SEC
 -Name Regulation S-X (SX)
 -Number 210
 -Section 02
 -Paragraph 19
 -Article 5

Reference 3: http://www.xbrl.org/2003/role/presentationRef
 -Publisher SEC
 -Name Regulation S-X (SX)
 -Number 210
 -Section 03
 -Paragraph 13
 -Article 9

</ElementReferences>
      <IsTotalLabel>false</IsTotalLabel>
    </Row>
  </Rows>
  <Footnotes />
  <NumberOfCols>1</NumberOfCols>
  <NumberOfRows>2</NumberOfRows>
  <HasScenarios>false</HasScenarios>
  <MonetaryRoundingLevel>UnKnown</MonetaryRoundingLevel>
  <SharesRoundingLevel>UnKnown</SharesRoundingLevel>
  <PerShareRoundingLevel>UnKnown</PerShareRoundingLevel>
  <HasPureData>false</HasPureData>
  <SharesShouldBeRounded>true</SharesShouldBeRounded>
</InstanceReport>
