In this paper, stability analysis of walking gaits and robustness analysis are developed for a five-link and four-actuator biped robot. Stability conditions are derived by studying unactuated dynamics and using the PoincarÃ© map associated with periodic walking gaits. A stable gait is designed by an optimization process satisfying physical constraints and stability conditions. Also, considering underactuation problem, a time-invariant control law is designed to track the stable motion of biped. Validation of proposed approach is achieved by numerical simulations. Moreover, the robustness of motion on the uneven surfaces and elastic contact model are investigated.