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This article presents the outcomes from analytical and experimental modelling, the power parameters of new burnishing of external cylindrical surfaces called spherical motion burnishing. The axes of the workpiece and the ring-shaped tool having toroidal acting surface intersect at an angle of 2 . The tool motion is superposition from a spherical motion and a rectilinear translation with respect to the workpiece. The method is implemented on lathes. The tool transfer angular velocity is assigned by the lathe spindle, and the relative one is a consequence from unknown manufacturing resistance. Analytical models of the power parameters of the new burnishing process have been obtained. The unknown manufacturing intensities in these models have been determined experimentally. For proving the authenticity of the proposed semi-analytical models a comparison of the results obtained for the axial force with the experimental ones has been made. For that purpose, the axial force has been measured by means of a strain gauge system. The comparison shows a good agreement.