In order to have a deep understanding of the kinematical characteristics of the displacer of free-piston stirling engine, the effects of gas force, which is driven by the displacer only, is analyzed. And the running experiment of displacer individually is designed. During the course of the experiment a new calculation formula for natural frequency of displacer is proposed. In this paper, the gas force acting on the displacer is analyzed in the case of leading or lagging displacement of piston. And the acting mechanism of gas force is stated by means of rotation vector decomposition. The results show that a part of gas force is regarded as gas spring. The gas spring and the mechanical spring are parallelly arranged and the natural frequency of the system increases in the case of the pressure wave in advance or delaying the displacement of piston less than 90°. But the gas force is regarded as gas inertia for ceand the natural frequency of the system decreases in the case of the pressure wave in advance or delaying the displacement of piston greater than 90° but less than 180°. And the higher the temperature of the heat source, the smaller the natural frequency of the system. The accuracy of the effects of gas force and calculation formula for natural frequency are verified by an experimental text on a free piston stirling engine which is designed by our laboratory.