A multicylinder internal combustion free-piston engine (FPE) with synchronized reciprocating plungers. The invention provides a solution for the problem of the slow engine speed typical of FPE's with heavy plunger mass. Bounce chambers fitted with sleeve valves control the engine's speed and stroke length. The invention's configuration prevents piston head-strikes and operates at standard compression ratios. Piston “pop-top” intake valves allow uniflow scavenging and connecting rod oil channels provide lubrication with no combustion chamber contamination. Poppet combustion head valves are operated by linear cams attached to the plungers. Hydraulic valve actuators implement variable valve timing under computer control.