The invention relates to a rotary engine. The internal cavity of the invention is made up of stator with elliptical cylinder or cinquefoil, cylinder type rotator, stator end cover, axis, bearing, base. The coaxial rotator and stator form 2-6 arc chambers, half of them is connected to the discharging aperture, and there has a firing device on the stator of the arc chamber; there arranges with spring and concave channel on the rotator symmetrically, the spring pushes the sliding board, another end of the sliding board is contacted to the internal surface of the stator and is sealed. The rotator rotates and absorbs the air into the aperture and is compressed, and the air enters the explosion chamber through the gap between the stator and the rotator, the firing device fires the gas, the generated explosion gas rotates to work around. The engine efficiency is high, the structure is simple, and the inlet and the discharging outlet need not single valve.