Abstract: The present invention relates to rotary engines of the type comprising a casing, assembled with two transverse end-plates and constituting a stator equipped with fluid-admission and exhaust tubes; a rotor associated with means for displacing said rotor in the stator so as to form working chambers with this latter; and rectilinear segments freely mounted in rectilinear grooves provided respectively along generator lines of said casing, corresponding to the separation edges of the working chambers on the internal surfaces of each end-plate, following at least three directions and forming a polygon surrounding the rotor-displacement means by virtue of a crossed arrangement, by overlapping of segments in pairs, especially along the radial directions corresponding to said casing segments and extending at least up to a segment of said polygon, each of these segments co-operating with other segments by slots or notches forming expansion clearances.