Free piston Stirling engines are structurally simple thermodynamic systems converting the heat into the reciprocating translational motion. In free piston Stirling engines mechanical and gas springs are used instead of the flywheels used in kinematic engines. In free piston Stirling engines one of the most important issues is keeping the amplitude of reciprocal motion of the displacer and piston under control. For the design of free piston Stirling engines, because of their structure, the dynamic and thermodynamic analyses are simultaneously conducted. The design and performance predictions of the engine is conducted via a dynamic-thermodynamic analysis including the masses of the dynamic components, constant of springs used in the system, hydrodynamic frictions, pressure forces exerting on the piston and displacer and damping forces caused by work transfer. In this study, via preparing a dynamic and thermodynamic simulation program, the analysis of a cold end connected gamma type free piston Stirling engine that will work in the temperature range of 350-700 K, have been performed. The working limits of the engine were predicted by means of examining the variation of power with the hot end temperature, spring constants of displacer and piston springs, rod diameter of the displacer, the working gas mass in the working volume of the engine and the damping constant due to the work transfer.