We have carried out a Monte Carlo simulation of a thin sample of the smectic-A phase of the Gay-Berne mesogen GB(4.4,20.0,1,1) sandwiched between two plates and subject to shear. The smectic layers are perpendicular to the confining plates and are pinned at the boundaries. The thickness of the samples studied ranges from about three to twenty molecules. The layers tilt progressively with increasing shear, but rearrange themselves at a critical shear. At this critical shear the layers melt near the center of the sample and reform with a reduced tilt consistent with the layer pinning at the walls. The pseudodynamics of this process as the smectic layers melt and are reformed have been followed during the simulation. The critical layer tilt at which slippage takes place tends to a constant value for thick samples, but for very thin samples the critical shear tends toward half a smectic layer, with a significantly reduced translational order near the sample center just before the critical shear. The simulation results are consistent with the predictions of the mean field theory of this phenomenon developed by Mottram et al.