We consider the problem of a mobile polymer chain anchored to a surface in the presence of a shear flow. We examine the case where the surface is solid, where it is the interface between two liquids, and where it is a membrane. Rodlike polymers and flexible polymers under good and theta conditions are studied. We find that at low shear rates the chain speed increases linearly with the shear rate. At higher shear rates a nonlinear relation is usually obtained due to chain distortion.