The costs and benefits of fighting in bovids are high in terms of injury and reproductive success, respectively. The breakage of a horn would curtail reproductive success permanently. Therefore, the horns of bovids should include sufficient material so that they are strong enough to be unlikely to break in fighting but without being too heavy to carry around. The forces developed during fighting were measured in a computerized analysis of film of blackbuck and bighorn sheep. All possible modes of failure were investigated using a mechanical analysis to see how the horns are most likely to fail.The maximum possible force developed during fighting is 3400 N for the bighorn sheep and 456 N for the blackbuck. Bending stress, shear stress, deflection, strain energy and critical crack lengths were calculated for the horns of these two bovids. Horns are most likely to fail in bending as indicated by safety factors. Most of the force is taken in compression due to the curvature of horns. Shear stresses are insignificant and deflections are negligible during the most forceful encounters.The safety factor in bending of the horn of the bighorn sheep is greater (10) than that of the horn of the blackbuck (3.4) because the forces are probably more variable and unpredictable in the fighting of the former.All of the energy of fighting is absorbed by the body musculature because horns store less than 1% of the energy produced in fighting as strain energy when they bend. Cracks and scratches mustbe more than 60% of the transverse basal dimensions of horns in order for there to be catastrophic failure at the maximum stresses developed during fighting.The horns of the blackbuck and the bighorn sheep appear to be minimum weight structures given the variability of the forces acting on them and are unlikely to break in fighting given the forces calculated from the analyses of films.