The present work studies a positive displacement rotary Stirling engine. Two simulation models for this rotary Stirling engine are developed. The first model applies the isothermal method, in which the gas at the engine expansion / compression chamber has the same temperatures of the thermal reservoir. The second model uses the control volume method, in which the engine is divided into five control volumes: the expansion and compression chambers, the heater, the chiller and the rotary chamber. For each control volume the equations of conservation of mass and energy and the equation of state, are applied. The system of ordinary differential equations resulting from the second model is integrated allowing to obtain the variation in the axis angle for all thermodynamic variables of the motor (pressure, temperature, etc.). Given the operating conditions and geometry of the rotating motor under study, the models provide global and transient results from angle to angle. Results from two models are confronted with theoretical results available in the literature.