Motion of a nonsingular flat wall in twisted planar nematic layers is investigated for a finite strength of the surface anchoring in the cell. The measurements of the wall velocity as a function of the rotation angle of the cell plate are performed. The theoretical calculations of the corresponding dependences performed for two different model anchoring potentials reveal that for thick samples the both potentials give almost the same results. For thin samples the calculation results for these potentials differ significantly. It is shown that the measurements of the wall velocity allow the determination of the anchoring strength and may be used for the reconstruction of the shape of the actual surface anchoring potential.