Exhibit 4.1

DESCRIPTION OF SECURITIES

The following description of the units of limited partnership interest (the “Units”) of Everflow Eastern Partners, L.P. (the “Company”) and the rights of holders thereof (each, a “Holder”) is summary only and is subject to the complete text of the Company’s Partnership Agreement (the “Partnership Agreement”).

Market

The Units are registered pursuant to Section 12(b) of the Securities Exchange Act of 1934, as amended. There is currently no established public trading market for the Units. At the present time, the Company does not intend to list any of the Units for trading on any exchange or otherwise take any action to establish any market for the Units. As of March 10, 2020, there were 5,492,967 Units held by 1,340 holders of record.

Distribution History

The Company commenced operations in February 1991. Management’s stated intention was to make quarterly cash distributions equal to $0.125 per Unit (or $0.50 per Unit on an annualized basis) for the first eight quarters following the commencement of operations. The Company paid a quarterly distribution every quarter from July 1991 through October 2015. The Company paid a cash distribution equal to $0.30 per Unit in April 2019. The Company intends to make a cash distribution equal to $0.25 per Unit in April 2020. The Company intends to make future distributions as cash flows warrant.

Repurchase Right

The Partnership Agreement provides that beginning in 1992 and annually thereafter the Company offers to repurchase for cash up to 10% of the then outstanding Units, to the extent Holders offer Units to the Company for repurchase (the “Repurchase Right”). The Repurchase Right entitles any Holder(s), between May 1 and June 30 of each year, to notify the Company that the Holder(s) elects to exercise the Repurchase Right and have the Company acquire certain or all Units. The price to be paid for any such Units is calculated based on the method provided for in the Partnership Agreement. The Company accepted an aggregate of 68,261 of its Units of limited partnership interest at a price of $0.11 per Unit pursuant to the terms of the Company’s Offer to Purchase dated April 30, 2018. The Company accepted an aggregate of 86,388 of its Units of limited partnership interest at a price of $1.50 per Unit pursuant to the terms of the Company’s Offer to Purchase dated April 30, 2019. The Company has determined that the price associated with the 2020 Repurchase Right, based upon the December 31, 2019 calculation, is estimated to be $0.86 per Unit.