A finite-element model was used to explore the relationship between connectivity density and the elastic modulus of trabecular bone. Six cubic specimens of trabecular bone, three prepared from human distal radii and three from L1 vertebrae, were imaged with synchrotron microtomography. The three-dimensional images were reconstructed into binary volumes of mineralized bone and soft tissue, and incorporated into the finite-element model. The relationship between three-dimensional connectivity and elastic modulus was explored by uniform thinning (atrophy) and thickening (recovery) of the trabecular bone. Though no functional relationship was found between connectivity and elastic modulus, there was a linear relationship, after a full cycle of atrophy and recovery, between the loss of elastic modulus and the overall loss of connectivity. The results indicate that recovery of mechanical function depends on preserving or restoring trabecular connectivity.