Push recovery is an important capability for a biped to safely maneuver in a real dynamic environment. In this paper, a generalized push recovery scheme to handle pushes from any direction that may occur at any walking phase is developed. Using the concept of walking phase modification, a series of systematic push recovery scheme that takes into account the severity of the push is presented. The result is that a bipedal robot could adapt to pushes according to the magnitude of disturbance and determine the best course of action. A number of push recovery experiments with different walking phases and push directions have been carried out using a 12-DOF humanoid robot model in dynamic simulations. The versatility and potential of the overall scheme is also demonstrated with the bipedal robot balancing on an accelerating cart.