In free piston Stirling engines the power generated by the engine is related to the length of the piston and displacer strokes. Length of strokes vary with respect to the hot end temperature, external load, charge pressure, rod diameter, stiffness of springs, masses of piston and displacer and static positions of the piston and displacer. When the length of displacer and piston strokes exceeds the estimated limits, some mechanical collisions occur between piston and displacer or displacer and cylinder. In this work, the dynamic model of a free piston Stirling engine working with closed and open thermodynamic cycles was derived and numerically solved for an optional pair of the piston and displacer masses. Safe ranges were investigated for the hot end temperature, charge pressure, damping coefficient of the piston motion, stiffness of the piston spring and area of the displacer rod. The stiffness of the displacer spring and static positions of the piston and displacer were optimized. Analysis indicated that, a free piston Stirling engine working with a closed thermodynamic cycle performs a stable operation within a small range of the hot end temperature and damping coefficient of the piston motion. By means of inverting the engine into an open-cycle engine, the limited range of the hot end temperature and the damping coefficient of the piston motion were partially enlarged. (C) 2010 Elsevier Ltd. All rights reserved.