The aim of this thesis is to present a model for studying the dynamic behaviour of scroll expanders. The latter are volumetric machines that generate mechanical power expanding high pressure gas\vapor in two or more variable volume chambers. The first step consists in the description of the device geometry, the purpose is the calculation of the expansion chambers volume. In this section, starting from the involute of the circle, are introduced all the quantities needed for the subsequent development of the model. After that is presented the thermodynamic model that allows to calculate the pressures and temperatures inside each chamber. In particular are presented the equations used to compute the working fluid leaks, the exchanged heat and the torque.