A new design method for selecting the physical parameters of a free piston Stirling engine (FPSE) is presented. The dynamics of FPSE are described in the form of a transfer function including the inherent feedback mechanism. The simplified Nyquist stability criterion is used to derive the operation condition, where the indices of the magnitude amplification factor (MAF) and the operation limit factor (OLF) are introduced in terms of the physical parameters. Further, a measure for the efficiency of the engine is defined as the damping ratio of the power piston system (DRP). Parametric studies of these quantities are carried out as well as benchmarking against the design values of the standard RE-1000 engine. A design method is presented that defines the physical parameters of an FPSE which is working at a given operation frequency.