We present results of Brownian dynamics simulations of polymer brushes under steady and oscillatory shear. The brush is sheared by a bare surface and the resulting solvent velocity and polymer dynamics are solved self-consistently. Under steady shear the deformation of the blush proceeds in two steps : chains tilt in the now direction followed by a physical thinning of the brush. The brush-effective viscosity increases upon compression to near 60% and decreases thereafter. We develop a scaling based on the Brinkman equation to explain the unusual trends in the viscosity. Upon introducing oscillatory shear now in the brush, we observe large increases in the normal stress and bead density near the upward surface. Shear-induced collisions of beads in the brush increase the osmotic pressure and thus give rise to these normal forces. The strain amplitude determines the dynamics during oscillatory now, and we develop scalings for the range of strain amplitude over which the normal stress increases occur. The simulation results for a single grafted layer are compared to the experiments performed by Klein et al. for the shearing of two grafted layers.