In this work we present a simple mathematical model for a ββ-type Stirling engine. Despite its simplicity, the model considers all the engine’s relevant thermodynamic and mechanical aspects. The dynamic behavior of the model equation of motion is analyzed in order to obtain the sufficient conditions for engine cycling and to study the stability of the stationary regime. The performance of the engine’s thermodynamic part is also investigated. As a matter of fact, we found that it corresponds to a Carnot engine.