Analytic determination of muscle force across human joints encounters an indeterminate problem. A new optimization approach, based on minimizing the upper bound of muscle stress, is introduced to obtain a unique solution. Mathematical and physiological justification of this new approach distinguishes it from previously described methods. A complex joint, the elbow, was studied. The results of muscle forces in resisting the elbow flexion moment were obtained and compared with electromyographic observation, as well as with solution from other optimizing techniques. The resultant humero-ulnar joint forces at various elbow joint positions are calculated. In normal daily activities, resultant joint forces of 0.3–0.5 times body weight are commonly encountered.