This paper is the last of a three-part series that investigates the architecture of cancellous bone in the main hindlimb bones of theropod dinosaurs, and uses cancellous bone architectural patterns to infer locomotor biomechanics in extinct non-avian species. Cancellous bone is highly sensitive to its prevailing mechanical environment, and may therefore help further understanding of locomotor biomechanics in extinct tetrapod vertebrates such as dinosaurs. Here in Part III, the biomechanical modelling approach derived previously was applied to two species of extinct, non-avian theropods, Daspletosaurus torosus and Troodon formosus. Observed cancellous bone architectural patterns were linked with quasi-static, three-dimensional musculoskeletal and finite element models of the hindlimb of both species, and used to derive characteristic postures that best aligned continuum-level principal stresses with cancellous bone fabric. The posture identified for Daspletosaurus was largely upright, with a subvertical femoral orientation, whilst that identified for Troodon was more crouched, but not to the degree observed in extant birds. In addition to providing new insight on posture and limb articulation, this study also tested previous hypotheses of limb bone loading mechanics and muscular control strategies in non-avian theropods, and how these aspects evolved on the line to birds. The results support the hypothesis that an upright femoral posture is correlated with bending-dominant bone loading and abduction-based muscular support of the hip, whereas a crouched femoral posture is correlated with torsion-dominant bone loading and long-axis rotation-based muscular support. Moreover, the results of this study also support the inference that hindlimb posture, bone loading mechanics and muscular support strategies evolved in a gradual fashion along the line to extant birds.