An external combustion engine including a rotary motor equipped with non-sliding vanes but conformable to the shapes of the envelopes within which they are contained and forced to operate and a combustion member comprising a sleeve in which a piston is free to reciprocate. The two end closures of the sleeve and the piston ends cooperate to form combustion chambers at both ends of the piston strokes. The motor compresses air for admission in the combustion chambers where fuel is burned and is also used for expanding the combusted gas resulting from the fuel combustion. The gas expansion produces more energy than is required to compress the air. The energy difference constitutes the energy yielded by the engine in the form of shaft power. The air admission, the combusted gas exhaust from the combustion member, the fuel injection and ignition are all timely controlled by the piston motion. The air compression and the gas expansion may be performed by a different set of vanes, but may also be performed by the same set of blades, depending upon the manner in which the motor is constructed. In one motor configuration, rigid blades are articulated to allow the blade conforming, whereas blades are flexibly constructed in another alternate motor configuration, to the same end.