It is well established that mechanical stimulation influences the differentiation of skeletal stem cells during healing of a bone injury. However, quantitative relationships between mechanical stimuli and cellular responses in skeletal healing have not been established. This dissertation sought to elucidate these relationships in several ways. First, a leading mechano-regulation theory, which postulates that shear strain and fluid flow are the principal mechanical stimuli that influence stem-cell differentiation, was evaluated in a novel scenario, that of a mechanically generated pseudarthrosis ("false joint"). In all previous tests of this theory, only situations in which bone healing progressed successfully were considered. In the present work, a numerical simulation based on this theory correctly predicted that an applied bending motion would result primarily in cartilage formation and, overall, a joint-like structure at the bony injury. However, this simulation was limited by assumptions about the geometry of the injury and the mechanical properties of the tissues. The second portion of this dissertation addressed these limitations by using micro-computed tomography (pCT) and microindentation to quantify the sample geometry and material properties. These data were used to create sample-specific finite element (FE) models of bony defects stimulated by a bending motion. The ensuing simulations indicated that the best agreement between simulation and experiment occurred when the assumed rate of healing was varied to hasten the development of a heterogeneous distribution of permeability, thus emphasizing the importance of fluid flow as mechanical stimulus. In the third portion of this dissertation, an alternative method, contrast-enhanced computed tomography (CECT), was developed that addressed the possibility of estimating the spatial distributions and material properties of the tissues in a non-destructive manner. Together, the methods of CECT and sample-specific FE modeling revealed the complexity of the inter-relationship between the healing tissues and their mechanical environment. By providing strong evidence that shear strain and fluid flow are mechanical stimuli for stem-cell differentiation, and by developing a set of methods that help establish a quantitative map between these stimuli and cellular responses, this dissertation brings us closer to being able to use mechanical cues to facilitate repair and engineering of skeletal tissues.