Based on the structural feature that rollers in the recirculating planetary roller screw mechanism has no helix angle, the raceway surface equations of the screw, roller and nut are established using the tangential contact conditions of the components. Solving the meshing equation yields the contact point position and the axial clearance between the surfaces. Then, the influences of the flank angle and pitch on the contact point position and axial clearance are discussed respectively. The results show that the contact point position on the screw-roller interface always deviates from the line between the screw and roller axis, and the contact point on the screw and roller is located toward the top of their thread. If the flank angle of the roller and the nut are equal, the contact point position on the roller-nut interface will be located at the tangent point of the pitch diameter of the two threads. Compared to the standard planetary roller screw mechanism, the recirculating planetary roller screw mechanism exhibits a smaller deviation angle at the contact point and a smaller difference between the contact radius and the nominal radius. Therefore, in applications where precise calculation is not required, the influence of the contact point position deviation on the recirculating planetary roller screw mechanism can be neglected.