We have studied the conformation of a polymer brush in equilibrium with a solvent that is subject to a shear flow. The interplay between the polymer brush and the hydrodynamic flow of the solvent has been modeled, with simple but largely justifiable approximations. The main technique used in our study is a Monte-Carlo simulation algorithm that is distinct from many standard numerical methods used in studies of polymer brushes in that it combines an off-lattice description of polymer brushes-the Edwards Hamiltonian-with a modification of the standard Metropolis Monte-Carlo transition probability to take into account the effective force acting upon the polymer molecules by the moving solvent. The conformation of the polymer brush, the configurations of each individual chain in particular, is investigated in detail. It is found that the significant response of the brush to the solvent shear flow manifests principally in the form of the chain tilting toward and stretching along the direction of the flow, whereas the overall conformational properties, such as the averaged local monomer density, and the linear span of the brush in the direction normal to that of the flow remain essentially unaffected by the flow. Such response can be understood both qualitatively and semiquantitatively in terms of a notion of the mechanical balance of the different physical forces involved, which was used in the theory of Rabin and Alexander (Rabin, Y.; Alexander, S. Europhys. Lett. 1990, 13, 49). The relevance of our study to some recent experiments is briefly discussed.