We have studied theoretically the role of an external constant shear on the extent of suppression oi composition fluctuations and stabilization of different ordered morphologies in block copolymer systems. The dependence of steady state structure factor on constant shear is calculated self-consistently in the weak segregation limit. The effect of shear rate on order-order and order-disorder transitions involving lamellar and cylindrical morphologies is computed. Previous theoretical work calculated effects to the lowest order in shear rate. This paper performs a numerical calculation that is not limited to small shear rates. This more general approach is required in order to explain experimental results. Our results are in good agreement with known experimental data and make new quantitative predictions. The controversy involving an apparent discrepancy between experimental data and previous predictions from perturbation analysis is resolved. (C) 1997 American Institute of Physics.