Abstract: An internal pressure engine comprises at least three like members called hedrons movable between two parallel end plates. Each of the hedrons has opposite end faces engaging the end plates, an inner face extending between the end faces and a sealing face disposed relative to the inner face at an angle equal to 360.degree. divided by the number of hedrons. The sealing face of each hedron engages the inner face of the next adjacent hedron so as to form a working chamber bounded by the end plates and the inner faces of the hedrons. The hedrons are supported and guided for translatory movement along rectilinear paths to vary the volume of the working chamber while maintaining the sealing faces of the hedrons in engagement with the inner faces of adjacent hedrons. Movement of the hedrons is synchronized by means of an oscillating member which is pivotally connected with each of the hedrons. Oscillatory movement of the synchronizing member is converted into rotary movement of a drive shaft by a crank mechanism.