An algorithm based on finite elements applied to digital images is described for computing the linear elastic properties of heterogeneous materials. As an example of the algorithm, and for their own intrinsic interest, the effective Poisson's ratios of two-phase random isotropic composites are investigated numerically and via effective medium theory, in two and three dimensions. For the specific case where both phases have the same Poisson's ratio (ν1 = ν2), it is found that there exists a critical value ν*, such that when ν1 = ν2 > ν*, the composite Poisson's ratio ν always decreases and is bounded below by ν* when the two phases are mixed. If ν1 = ν2 < ν*, the value of ν always increases and is bounded above by ν* when the two phases are mixed. In d dimensions, the value of ν* is predicted to be using effective medium theory and scaling arguments. Numerical results are presented in two and three dimensions that support this picture, which is believed to be largely independent of microstructural details.