A rotary piston engine is provided. The rotary piston engine includes a shell and a rotor, the rotating rotor is arranged in the shell and divides a rotor cavity into compression chambers with a variable volume, a plurality of combustion chambers rotating around a main shaft of the rotor are arranged on an outer ring of the shell, and any one of the plurality of combustion chambers is communicated with the compression chambers; the plurality of combustion chambers are in a transmission connection with the main shaft of the rotor via a transmission system, and each of the plurality of combustion chambers drives the main shaft of the rotor to rotate by a combustion of a compressed combustible gas mixture. The shell includes an upper cylinder cover and a lower cylinder cover, and a boss of the upper cylinder cover is fitted with a spigot of the lower cylinder cover.