The rotary engine includes a circular stator, a circular rotor rotating about the stator; the rotor and the stator being separated by a circular cylinder and at least one element with two flanges. The rotor includes two compression pistons attached to the inner surface of the rotor. These two pistons are located at the two extremities of a first diameter of the rotor and kept substantially in contact with the outer surface of the stator. The stator includes a recess at each extremity of a diameter. Each recess forms a compression chamber with the compression piston positioned at the end of the recess in the direction of rotation of the rotor and one of the flanges of the element with two flanges, referred to as the cylinder head flange. The motive force is applied to the compression piston when the pressure of the gases inside the compression chamber is suddenly increased to a predefined value.