Osteoporotic fracture incidence and underlying risk factors like low peak bone mass are heritable, but the genetic basis of osteoporosis remains poorly understood. Based on beam theory, stating that mechanical properties of a structure depend on both the amount and quality of the constituent materials, we investigated the relationship between whole bone mechanical properties and a set of morphological and compositional traits in femurs of eight inbred mouse strains. K-means cluster analysis revealed that individual femora could be classified reliably according to genotype based on the combination of bone area (tissue amount), moment of inertia (tissue distribution), and ash content (tissue quality). This trait combination explained 66-88% of the inter-strain variability in four whole-bone mechanical properties that describe all aspects of the failure process, including measures of brittleness. Stiffness and maximum load were functionally associated with cortical area, while measures of brittleness were associated with ash content. In contrast, work-to-failure was not directly related to a single trait but depended on a combination of trait magnitudes. From these findings, which were entirely consistent with established mechanical theory, we developed a hierarchical paradigm relating the mechanical properties that define bone fragility with readily measurable phenotypic traits that exhibit strong heritability. This paradigm will help guide the search for genes that underlie fracture susceptibility and osteoporosis. Moreover, because the traits we examined are measurable with non-invasive means, this approach may also prove directly applicable to osteoporosis risk assessment.