A free piston Stirling cycle machine is illustrated by an engine that utilizes an axially movable displacer subjected to working gas pressures. A primary hydraulic circuit hydrostatically couples a displacer drive rod integral with the displacer to a counterbalance illustrated in the form of a scotch yoke. The counterbalance stabilizes and controls the Stirling cycle engine by constraining the displacer's reciprocating axial motion in a repetitive pattern. A throttling valve interposed in the primary hydraulic fluid circuit is used to adjustably resist displacer motion as required by engine operating conditions. A secondary hydraulic circuit is provided together with a bellows assembly between the working gas and power pistons to convert changes in working gas pressure to usable power output in the form of pumped hydraulic fluid.