A vane cell pump has a rotor mounted in a pump housing and driven by a shaft, multiple vane plates mounted in the outer circumference of this rotor, and an outer ring that surrounds the rotor and the vane plates, whereby this ring is disposed either directly in the pump housing, or in a setting ring that can be moved in the pump housing, along predetermined paths. The vane cell pump has transverse grooves disposed in the cylinder mantle surface of the rotor, between the bearing grooves of the vane plates, running over the entire rotor width, disposed parallel to the bearing grooves of the vane plates, spaced apart from the bearing grooves by a bearing crosspiece. These transverse grooves have a non-symmetrical cross-section progression, which has a low point in each cell chamber, which point is always disposed behind the cell chamber center axis, seen in the direction of rotation.