In this paper, a novel foot force distribution algorithm for hexapod walking robots is presented. The considered hexapod robot has fault-tolerant tripod gaits with a failed leg in locked-joint failure. The principle of the proposed algorithm is to minimize the slippage of the leg that determines the stability margin of the fault-tolerant gaits. The fault-tolerant tripod gait has a drawback that it has less stability margin than normal gaits. Considering this drawback, we use the feature that there are always three supporting legs, and by incorporating the theory of Zero-Interaction Force, we calculate the foot forces analytically without resort to any optimization technique. In a case study, the proposed algorithm is compared with a conventional foot force distribution method and its applicability is demonstrated.