The goal of this paper is to investigate the fluid flow analysis in a novel multilayered finned reciprocating compressor, adopting a so-called “pneumatic-Electric” analogy using a lumped methodology. This machine includes two sets of concentric annular fins with different diameters: the mobile fins are pushed into the space between the stationary fins through a driver shaft and compress the air trapped in the interconnecting annular chambers. Considering pressure as effort and mass flow as the flow variable, the equivalent electric circuit was developed to represent the behavior of the pneumatic system. The governing state space equations are derived and simulation results are presented.