A Stirling engine with internal regenerator and integral geometry for heat transfer and fluid flow has a displacer piston with a plurality of cavities traversing through the displacer piston and arranged in a specific cross sectional geometry. A heater head has heater fin protrusions that are arranged in the specific geometry, and a cooling bridge has cooler fin protrusions that are in the specific geometry. The displacer piston alternates between the heater head and the cooling bridge, with the cavities of the piston alternately enveloping the heater protrusions and the cooling protrusions, providing more efficient heat transfer to and from the working fluid. Each cavity in the displacer also contains a regenerator core, further improving heat transfer efficiency. The heater fin protrusions may also contain thermally conductive cores. A bellows assembly may also be used to seal the displacer piston from the heater head in order to reduce unswept volume.