We tackle the problem of a biped running over varied and unknown terrain. Running is a necessary skill for a biped moving fast, but it increases the challenge of dynamic balance, especially when a biped is running on varied terrain without terrain information (due to the di?culty and cost of obtaining the terrain information in a timely manner). To address this issue, a new dynamic indicator called the sustainable running criterion is developed. The main idea is to sustain a running motion without falling by maintaining the system states within a running-feasible set, instead of running on a periodic limit cycle gait in the traditional way. To meet the precondition of the criterion, the angular moment about the center of gravity (COG) is restrained close to zero at the end of the stance phase. Then to ensure a small state jump at touchdown on the unknown terrain, the velocity of the swing foot is restrained within a specifi c range at the end of the fl ight phase. Finally, the position and velocity of the COG are driven into the running-feasible set. A fi ve-link biped with underactuated point foot is considered in simulations. It is able to run over upward and downward terrain with a height difference of 0.15 m, which shows the effectiveness of our control scheme.