Based on the need for mechanistic approaches in studying mechanical structure-function relationships for trabecular bone, the goal here was to demonstrate the power of simple models to interpret experimental data on the mechanical behavior of trabecular bone. Modulus, yield strain, and apparent density data were obtained for specimens loaded on-axis (parallel to the principal trabecular orientation) without end-artifacts, taken from the human vertebral body and bovine proximal tibia. Closed-form solutions based on open and closed on-axis cellular solid models were then used to analyze these data. Results indicated that the slope of the modulus-density regression depends on both the density and general architecture of the bone and therefore depends on anatomic site. This implies that pooling data from different sites may be invalid if the purpose is to determine underlying deformation and failure mechanisms solely from statistical regression analysis. Further, structural parameters that might explain inter-specimen variations in modulus for one anatomic site may not apply to another due to the sitespecificity of such parameters. Finally, the analyses provided plausible predictions of the elastic modulus (13 GPa) and yield strains (tension, 0.78%;​ compression, 1.09%) of trabecular tissue material. Given the success of this analytical-experimental approach in studying many aspects of the structure-function relationships, it is recommended that future biomechanical studies of trabecular bone exploit this synergy whenever possible.