This paper describes the overtuming critelia of rigid bodies under an earthquake excitation. At first, we re-arranged the state and transition conditions for the motion of 3-D rigid body and gave the formulations in order to analyze the motion numerically. The modes of the motion are classified into six types; rest, slide, rocking, slide rocking, translation jump and rotation jump. An effect of input ground motion on the overtuming of the rigid body is investigated by changing the amplitude and the frequency of input accelerations and velocities. Finally, we proposed the criteria of the overtuming for the given input acceleration amplitude and velocity amplitude.