Rotary piston machine

A rotating piston machine with a housing (10) and a piston (12) which piston is rotatably arranged in a hollow space of the housing (10) and is rotatably fixedly connected to a shaft (18) passing through the housing, with the housing (10) having at least one inlet and one outlet channel (32) for the delivery and exhaust of a working fluid to and from the hollow space, characterized in that the hollow space has the shape of a section of a cylindrical annular space (14) coaxial to the shaft (18) and defined by a coaxially extending radially outer boundary wall and a coaxially extending radially inner boundary wall of the housing, that the piston (12) is formed as an annular piston in the shape of a cylindrical tube section, which piston is received in the annular space (14) of the housing (10) and is guided for axially shiftable movement, and that the end surfaces (20, 26) of the annular space (14) and of the annular piston (12) which face one another are formed as continuous wave surfaces with amplitudes directed parallel to the machine axis, wherein inlet and outlet openings (36,38) lie in at least one of the boundary walls of the annular space, within an axial region defined adjacent each axial end of the piston by the maximum axial spacing of the end surfaces (20,26) facing one another.