A novel Brownian dynamics method has been developed to simulate the properties of polymer brushes under shear. Simulations of 100 chains with a chain length of 100 segments have been carried out for a range of shear rates. Compared to previous methods there is a substantial saving in computational time as the self-consistent molecular field method has been chosen to calculate the volume interactions between polymer segments. An important criterion for observing significant deformations of the brush is that the chains must be stretched to beyond the Gaussian threshold. Density profiles and end segment distribution functions for the grafted chains have been determined and show a collapse of the brush under shear in a way similar to that in which a brush contracts in a poor solvent. In particular, the free ends of the chains become concentrated in a narrow region at the periphery of the brush. The number of chains that are affected by shear has also been calculated and shows that there is a progressive transmission of shear into the brush.