This paper presents a hierarchical controller and extracts the singular configurations based on underactuated system and optimal distribution of forces. Unlike multi-legged and large-sole robots, biped robot with point contact cannot maintain a stable standing state, much less to adjust attitude and resist external impact. The support domain of point-foot bipedal robot degenerates into a line segment consisting of two footholds, introducing the underdactuated characteristic that challenges traditional algorithms based on polygonal domains and full variable optimization. To fully exploit the dynamic connection between support line and balance control, the accurate model is established as feedforward terms using virtual leg and floating reference system. The dynamics model is decomposed into an underactuated module and a force distribution module for hierarchical control, in which the former determines the control forces of base and the singularity corresponding to robot configuration, and the latter distributes forces on each leg according to its capability by solving a quadratic programming with constraints. The results verify the advanced stability of attitude adjustment and impact from external force of biped robot with point contact comparing to model predictive control, which is improved based on robot’s singular configuration.