Abstract A Stirling engine develops work output from a thermal input. It is a quiet pollution free engine, which can use any heat source, including solar power. The piston-displacer mechanism is essentially a vibrating spring mass system and can be dynamically modelled, leading to a set of coupled nonlinear ordinary differential equations. The inadequacies of previous linear approaches are discussed and it is shown that the inclusion of a nonlinear load will lead to stable periodic motion as desired.