The constrained free-energy functional for deformed polymer systems is derived in a regime of small fluctuations. The free energy contains an elastic contribution due to chain deformation as well as the usual Ginzburg-Landau form. Up to terms quadratic in fluctuations, the linear elastic modulus tensor is obtained. We find that the shear modulus scales with the concentration in the same way as that suggested by scaling arguments in the mean-field regime. The elastic Poisson ratio is 1/2 for the dilute system and decreases as the volume fraction increases. In the melt limit, where the volume fraction is close to unity, the Poisson ratio is down to 0.2. (C) 1997 American Institute of Physics.