This work presents the novel peristaltic compressor, which has the potential to improve compressor efficiency by eliminating losses due to valves and over/under compression. This compressor operates by means of a progressively actuated diaphragm that compresses vapor and stimulates flow through a cylindrical chamber. In this study, we present a mechanistic chamber model of the compressor. A geometric model is developed along with the fundamental thermodynamic equations that describe compression as well as sub-models describing mass flow, leakage, and heat transfer. Additionally, validation of the model is presented using data from a reconfigurable prototype compressor using air as the working fluid. The reconfigurable prototype is operated with volume ratios ranging from 1.5 to 9 at pressure ratios ranging from 1 to 2.1. Each test is repeated 6 times and the experimental uncertainty of each test is within 5%. The mechanistic chamber model of the peristaltic compressor predicts the experimental mass flow rate and volumetric efficiency within 10% MAPE.