A rotary engine wherein the engine functions of intake, compression, combustion and exhaust are performed in four separate chambers disposed around the periphery of a cylindrical rotor rotating inside a case. The four chambers are formed by two radially extending pistons on the rotor and an annular disk which rotates around and in synchronism with the rotor. Openings are provided in the disk to allow passage of the rotor pistons through the disk. Fuel and air mixtures provided to the intake chamber are transferred to the compression chamber as the rotor pistons pass through the disk. Compressed fuel and air mixtures are transferred to a storage chamber and then to the combustion chamber for ignition of the mixtures. A reciprocable piston in the storage chamber forces the mixture into the combustion chamber without substantial loss of compression. Products of combustion are transferred from the combustion chamber to the exhaust chamber as the rotor pistons pass through the disk, and are expelled from the contracting exhaust chamber through an exhaust port.