The Stirling engines are inherently efficient; their thermodynamic cycles reach the Carnot efficiency. These technologies are suitable to operate under any low temperature difference between the hot and the cold sources. For these reasons, these engines can be considered as reliable power conversion systems to promote the conversion of low-grade waste heat generated by industrial plants. The need of a model to predict the behavior of these engines is of primary importance. Nevertheless, a great difficulty is encountered in developing such a model since it is not simple to take into account coupled thermodynamic and dynamic effects. This is the main reason why several models make use of electrical analogies to describe Stirling engines (in particular, free-piston machines): by assuming the pressure equivalent to a voltage and the flow rate to an electrical current, a coupled dynamic-thermodynamic analysis of the engine can be performed. In this paper, an electrical circuit whose behavior is equivalent to that of the engine is derived from the electrical analogy theory. To this aim, we propose an electrical analogy model based on the three conservation laws (mass, momentum and energy). Since limited experimental information is available in the open literature, the results obtained with the proposed model are compared with the experimental data collected at the NASA Lewis Research center for a free-piston Stirling engine i.e., the RE-1000 engine.