Abstract: This invention relates to rotary hydraulic devices of the volumetric or displacement pump type, having a stator and a rotor and vanes axially sliding in the rotor, the stator comprising at least one bottom surface presenting a variable number of recesses therein with ramps and rectilinear zones suited to the operation, said vanes following said bottom surface. In accordance with the invention, the vanes are equipped with an integral or inset base, with end lobes of cylindric shape having a radius of curvature corresponding to that of the milling cutter used for machining the stator. Access to the recesses occurs by means of two ramps corresponding to the lobes of cylindric shape of the vane bases.