The method of self-consistent Brownian dynamics developed recently has been adapted to simulate the properties of bimodal polymer brushes under shear. Simulations of three systems with different compositions have been carried out for a range of shear rate values. In the absence of shear, the free ends of short and long chains are mostly found in different sublayers inside the brush. Similar to the collapse of monodisperse brushes, we observed under shear a collapse of the outer sublayer, which is composed of long chains. Short chains are not stretched and inclined if the shear is not strong enough to cause a considerable intermixing of their free ends with the free ends of long chains in the direction perpendicular to the grafting surface. When the shear becomes very strong such intermixing occurs, and all chains are stretched and inclined in the shear direction. The number of chains, directly affected by shear, is very small. However, the shear stress is transferred into the brush below the flow penetration level owing to the rotation of the free chain ends.