Gas action effect of free piston Stirling engine (FPSE) is very important to solve the key problem of start-up and find the way to increase its efficiency. The gas force is a key force to free FPSE. In this paper, the gas action effect has been analyzed by the method of rotation vector decomposition. It is found that the gas forces of piston and displacer can be decomposed into two forces, one component acts as motivation force resisting the damping force to output power, the other acts as spring force or inertia force according to the phase angle of pressure wave to displacements of the displacer and piston. Only when the motivation components of both piston and displacer resist their damping forces, will the FPSE be start-up and work stably. And only when the spring force is approximately equal to inertia force of piston, will the piston need the smallest gas spring force and nearly all the gas force be put for the alternator, meanwhile the engine outputs the maximum work. In the perfect condition, the optimal phase angle of the reciprocating movements of the displacer and piston ahead of the pressure wave are 180 degrees and 90 degrees respectively. The analyses above are verified by a series of experiments on a FPSE designed by our laboratory. (C) 2015 Elsevier Ltd. All rights reserved.