Polymers end-grafted to a surface in the presence of a shear flow are studied by molecular dynamics simulations. The solvent velocity field is observed to penetrate only a short distance into the brush consistent with predictions based on self-consistent field theory. The deformation of the brush is small except when the shear rate γ is very large. In this limit, while some of the polymer chains are stretched in the direction of flow, the brush height actually decreases slightly, in contrast to several theoretical predictions. When two surfaces bearing end-grafted chains are brought into contact, the normal force increases rapidly with decreasing plate separation, while the shear force is significantly smaller. For low relative velocity v
of the two walls, the surfaces slide pass each other with almost no change in the chain's radius of gyration or the amount of interpenetration, while for very large v
, there is significant stretching and some disentanglement of the chains. The results are in qualitatively good agreement with recent experiments using the surface force apparatus.