PURPOSE: To obtain a rotary machine for effecting compression/expansion with excellent efficiency by mounting a rotor provided with radial cylinders in a housing and limiting the piston stroke in the cylinder to be non-circular at the side of the housing.

CONSTITUTION: A rotor 1 has four radial cylinder cavities 3 passing through a port 4 through the central portion of the rotor 1. Pistons 5 with shoes or bearing elements 7 are arranged in opposite relationship in the cavities 3. The shoe or bearing element 7 is preferably contacted with the inner surface of an elliptical race or external edge 8. The race or external edge 8 engages with a housing. A variable-volume chamber is formed between the cavity 3 and the inner surface of the piston 5 to effect induction/compression/expansion/ exhaust strokes when used in an internal combustion engine. In this way, it is possible to obtain a rotary machine with excellent efficiency.