We caluclate the free energy of surfaces coated with grafted polymers in a solvent. We use a self-consistent field (SCF) method appropriate for weak excluded-volume interactions and at moderately high surface coverage. We give the exact solution for the classical limit öf our SCF equations which shows that, at high molecular weight, the concentration profile appraoches a parabolic form rather than the step-fucntion suggestd by Alexander and de Gennes. Accodringly, the energy required to slightly compress the brush varies as the cube of the compression distance. An extension of the method to the good-solvent, semidilute regime is described.