A free piston engine is configured with a pair of opposed engine cylinders located on opposite sides of a fluid pumping assembly. An inner piston assembly includes a pair of inner pistons, one each operatively located in a respective one of the engine cylinders, with a push rod connected between the inner pistons. The push rod extends through an inner pumping chamber in the fluid pumping assembly and forms a fluid plunger within this chamber. An outer piston assembly includes a pair of outer pistons, one each operatively located in a respective one of the engine cylinders, with at least one pull rod connected between the outer pistons. The pull rod extends through an outer pumping chamber in the fluid pumping assembly and forms a fluid plunger within this chamber. Piston stoppers are provided to prevent over-travel of the piston assemblies.