In Stirling engines designed for continuous work conditions, clearance seals are usually used to avoid excessive wear and hence to extend the service life. This causes a gas leakage between the compression space and the expansion space through the displacer's clearance and also a gas leakage between the compression space and the bounce space through the power piston's clearance. In this study, we propose an unsteady analytical model to calculate the gas leakage mass flow rate by considering an oscillating flow in the annular clearance and to evaluate the power lost in both locations. Finally, the sensitivity to some relevant parameters is discussed.