This paper presents the results of a theoretical analysis of a heat exchanger design for the challenging application of a small-scale modified Linde-Hampson cycle liquid air energy storage system (LAESS). A systems engineering approach was taken to determine the best heat exchanger alternative for incorporation into an existing LAESS. Two primary heat exchanger designs were analyzed and compared: a finned tube heat exchanger (FTHE) design and a printed circuit heat exchanger (PCHE) design. These designs were chosen as alternatives due to the gas-to-gas cooling that occurs in the heat exchanger, and material selection was based on the requirement for the heat exchanger to withstand the cryogenic temperatures required for the system to produce liquid nitrogen. Thermodynamic analysis was conducted using the ε-NTU method and fin theory to determine the dimensional requirements for the finned tube heat exchanger and a trade-off study was conducted to compare the alternatives. Based on the results from the study, the PCHE was the preferred alternative due to an inherent small footprint, comparable cost to manufacture, simple integration into the LAESS and inherent safety features that are critical when working with high pressure systems. Future work will include subsystem and system integration and testing to obtain a consistently functional prototype that produces liquid nitrogen.