In recent years, a number of mathematical theories have been proposed relating bone development, maintenance and functional adaptation to the bone’s mechanical loading history. In this dissertation, novel applications are developed for an existing strain energy-based adaptation theory and the suitability and implications of this theory are carefully explored. The theory is reformulated to include phenomena not accounted for in the existing formulation, extending the range of issues to which it can be addressed. For the first time, a bone adaptation theory is used to examine adaptations within the pelvis. The simulations reproduce the normal internal structure of the pelvis, indicating that the structure of the adult pelvis is adapted to normal adult loading. Simulations involving acetabular components for total hip arthroplasty dem onstrate a strong influence of bone/im plant interface conditions on long-term patterns of trabecular adaptation following joint replacement, and suggest new directions in component design. Internal adaptation problems are highly nonlinear with coupled degrees of freedom, but a simple analysis is shown to give reasonable estim ates of the critical tim e step for forward Euler implementations. Existing adaptation theories predict long-term patterns of bone adaptation, but do not accurately represent the tim e course of short-term adaptations to abrupt changes in the typical daily loading. The theory is reformulated to account for biological lags in the cellular response to altered loading, resulting in more realistic and useful predictions of short-term adaptations. A new approach is developed to examine mechanical influences on long bone cross-sectional gometric adaptation. Simulations indicate that bending moments strongly influence cross-sectional shape, but tend to produce unrealistic geometric instabilities. The addition of torsional moments stabilizes the simulations and produces realistic cross-sectional geometries, indicating that torsional loads may play a greater role in cross-sectional development than previously thought. Simulations involving both bending and torsional loads are consistent with experimentally observed patterns of bone adaptation to altered loading, both during growth and following skeletal maturity. Finally, an alternative theoretical derivation for cortical bone adaptation is presented based on energy dissipation data. The energy dissipation approach predicts additional behaviors not represented by existing strain energy-based formulations, such as a difference between peak tensile and compressive bone surface strains. This dissertation establishes new approaches for examining both basic and applied aspects of bone adaptation, and extends the range of issues which can be addressed by bone adaptation simulations.