A continuum model describing the spinodal decomposition of polymer blends under externally applied shear has been developed. Numerical simulations were conducted for two-dimensional Couette flow. The morphology of the resulting polymer blend was established by competition between diffusion, forced convection and the internally driven flows which arise from concentration gradients. Diffusion and the internal flows tended to give compact and particulate morphologies. Externally imposed shear tended to give elongated structures, but a dynamic equilibrium was sometimes established. If flow was stopped, the elongated structures were comparatively stable when subjected only to diffusion (Ostwald ripening) but were unstable when subjected to the internally driven flows. These results represent a first attempt at understanding the structures of polymer blends prepared in melt processing equipment.