The non-equilibrium behaviour of concentrated colloidal dispersions is studied using Stokesian Dynamics, a molecular-dynamics-like simulation technique for analysing suspensions of particles immersed in a Newtonian fluid. The simulations are of a monodisperse suspension of Brownian hard spheres in simple shear flow as a function of the Péclet number, Pe, which measures the relative importance of hydrodynamic and Brownian forces, over a range of volume fraction 0.316 [les ] ϕ [les ] 0.49. For Pe < 10, Brownian motion dominates the behaviour, the suspension remains well-dispersed, and the viscosity shear thins. The first normal stress difference is positive and the second negative. At higher Pe, hydrodynamics dominate resulting in an increase in the long-time self-diffusivity and the viscosity. The first normal stress difference changes sign when hydrodynamics dominate. Simulation results are shown to agree well with both theory and experiment.