A rotary fluid machine 10 has a rotor 12, a stator 14, and a plurality of gates. The rotor 12 and stator 14 are rotatable relative to each other and arranged one inside the other to define a working chamber 18 there between. Gates 16 are supported in radial gate slots 20 formed in the rotor 12 and cyclically extend from and retract into the gate slots 20 as the rotor 12 rotates about stator 14. A plurality of demountable lobes is supported on an outer circumferential surface 24 of stator 14. The surface 24 forms a surface of the working chamber 18. Circumferential surface 24 is composed of an intermediate surface 48 which extends in an axial direction and opposite curved surfaces 46. The gate 16 has opposite rounded corners 130 separated by an axial planar surface 132. The shape and configuration of the gate 16 and corresponding is made to match that of the outer circumferential surface 24 so that when the axial surface 132 lies substantially adjacent and parallel to intermediate surface 48 each of the curved surfaces 130 lie closely adjacent to and substantially parallel with the concavely curved surfaces 46.