Plausible poses were identified for the hind limb of Tyrannosaurus rex and three other non-avian theropod dinosaurs at mid-stance of locomotion using constraint-based exclusion. This new method, validated by analysis of two species of birds, involves applying demonstrably realistic geometric and kinetic (force-based) constraints from extant animals to exclude, rather than include, potential poses. Starting with a “configuration space” of millions of candidate poses, we used a step-wise series of criteria to constrict the volume to a small subset of solutions, which can serve as starting points for reconstructing complete stride cycles. It was found that the maximum relative mid-stance limb force, as well as the relative number of configurations at lower forces, decreased with increasing body size. Constraint-based exclusion restricted Tyrannosaurus to a narrow region of neither very columnar nor very flexed poses that may have allowed relatively slow running, but no reasonable combinations of input parameters and pose produce forces large enough for high speeds. This analysis shows that skeletal information alone has limited value for discerning mid-stance poses. Despite additional assumptions, unpreserved parameters such as masses, forces, and moments are required to study a fossil as a functioning animal, rather than as a moving set of bones. Constraint-based exclusion is a transparent, reproducible framework for evaluating functional hypotheses in dinosaurs and other taxa.