The dynamic characteristics of a free-piston stirling engine(FPSE) with regard to the working frequency is investigated from theoretical and experimental studies. The FPSE is modeled as a two degree-of-freedom linear vibration system. A theoretical expression on the working frequency is derived from the instability condition for self-excitation based on the linear vibration model. A ${gamma}$-type free-piston stirling engine is fabricated for experimental studies, and its working frequency is measured on various heater temperatures. Comparisons between the theoretical and experimental results reveal that the working frequency of the test FPSE depends on both the temperature of the compression space and the temperature difference between the expansion and compression spaces.