We examined the sensitivity of internal tibial forces and moments during running to different subtalar/ankle moment constraints in a static optimization routine. Seventeen participants ran at 2.20, 3.33, and 4.17 ms−1 while force and motion data were collected. Ankle joint contact force was estimated using inverse-dynamics-based static optimization. Three sets of joint moment constraints were tested. All sets included the flexion–extension and abduction–adduction moments at the hip and the flexion–extension moment at the knee but differed in the constraints used at the subtalar/ankle: (1) flexion–extension at the ankle (Sag), (2) flexion–extension and inversion–eversion at ankle (Sag + Front), and (3) flexion–extension at the ankle and supination–pronation at the subtalar (Sag + SubT). Internal tibial forces and moments were quantified at the distal one-third of the tibia, by ensuring static equilibrium with applied forces and moments. No interaction was observed between running speed and constraint for internal tibial forces or moments. Sag + SubT resulted in larger internal mediolateral force (+41%), frontal (+79%), and transverse (+29%) plane moments, compared to Sag and Sag + Front. Internal axial force was greatest in Sag + Front, compared to Sag and Sag + SubT (+37%). Faster running speeds resulted in greater internal tibial forces and moments in all directions (≥+6%). Internal tibial forces and moments at the distal one-third of the tibia were sensitive to the subtalar and ankle joint moment constraints used in the static optimization routine, independent of running speed.