:This paper presents a stability analysis of the free-piston Stirling engine and linear alternator power generation system. Since such a system operates under sustained mechanical oscillations, stability of the system is important for proper operation, and as a criterion in selecting the tuning capacitor. The stability criterion of the system is that the rate of change in power dissipation and electric power output is always faster than the rate of the power generated by the engine. The dynamic equations and model of the system are developed in this paper. Frequency domain analysis and Bode plot techniques are utilized in the study. The stable operating frequency region corresponding to different levels of power output are then determined.