Abstract: The rotary machine can be used as a rotary internal combustion engine and as a pneumatic or hydraulic pump. The rotary machine comprises a housing in the form of two intersecting cylinder parts of different diameters having parallel axes. A rotor is received in the housing coaxially with the smaller-diameter cylinder and comprises at least two segmental rotor parts provided with annular rotor covers. At least two pairs of annular elements are provided engaging with the segmental rotor parts. Pivotal elements are interposed between the annular elements of each pair. A driving member is accommodated movably in the openings of the pivotal elements. The axis of rotation of the driving member is coincident with the axis of the larger-diameter inner cylindrical surface of the housing.