Using Monte Carlo, simulations of an off-lattice model, we study the elastic properties. of polymer-grafted membranes. Our results are found to be in good agreement with those predicted by the classical path approximation of the self-consistent field theory and scaling theory based on de Gennes' blob picture. In particular, we found that when the membrane is grafted on both sides by brushes with same molecular weight N and grafting density sigma, the excess bending modulus induced by the polymers scales as N(3)sigma(alpha) where alpha is consistent with 7/3, as predicted by the self-consistent field theory, and 5/2, as predicted by the scaling theory. When the polymers are grafted to one side of the membrane only; the membrane bends away from the polymers with a spontaneous curvature with a scaling that, is consistent with both scaling and self-consistent field theories. When the thickness of the brush exceeds the membrane's spontaneous radius of curvature, the bending modulus approaches a constant which is of the same order as the bending modulus of the bare membrane. (C) 2004 American Institute of Physics.