The purpose of this study was to test quantitatively the hypothesis that, as runners run along a more sharply curved track, greater torsional moments act on their tibiae. Six male participants were asked to run along a straight track and along counterclockwise curved tracks with turn radii of 15 m (gentle) and 5 m (sharp) at 3.5 m s–1. Data were collected using two high-speed cameras and force platforms. Each participant’s left (corresponding to the inside of the curves) foot and tibia were modeled as a system of coupled rigid bodies. For analysis, net axial moments acting on both ends of the tibia were calculated using free-body analysis. The torsional moment acting on the tibia was determined from the quasi-equilibrium balance of the tibial axial moments based on the assumption that the rate of change of the angular momentum about the tibial axis was negligible. The results showed that the torsional moments, which were in the direction of external rotational loading of the proximal tibiae, increased as the track curvature became sharper. Furthermore, the mean value of the maximum torsional moments, while running on a sharply curved track (28.5 Nm), was significantly higher than the values obtained while running on a straight track (11.0 Nm, p < .01) and on a gently curved track (12.2 Nm, p < .01). In conclusion, the present study has quantitatively confirmed that as runners run along a more sharply curved track, greater torsional moments act on their tibiae. The findings imply that athletes prone to tibial running injuries such as stress fractures should avoid repetitive running on sharply curved paths.