Free-Piston Stirling Engines (FPSEs) have recently attracted attention as a promising energy conversion technology because of their desirable characteristics such as high efficiency, high reliability, and easy and quiet operation. FPSE are truly a closed cycle system that works using variations in the internal pressure to drive the power piston that is connected to the reciprocating magnets in a linear alternator for energy conversion. The lack of manual linages and the use of clearance seals in a FPSE increase both the system's reliability and lifespan, as there is no contact or wear on the seals. These desirable attributes coupled with the fuel independence of FPSE makes them ideal candidates for use in remote power generation applications, particularly where maintenance is a high concern such as in NASA deep space missions, solar power generator, and combined heat and power systems. This chapter presents an introduction to FPSE along with a brief review of the underlying thermodynamics and Stirling cycle analysis. The general engineering analysis and numerical modeling approaches of Stirling engines will be discussed, followed by a section of engine design and efficiency calculations.