Most of the conventional legged robots are based on rigid body parts connected by high-torque actuators and a sophisticated control scheme to achieve stable running locomotion. The energy-efficiency of such robots is roughly 10-100 times lower than that of animals. Recently, there has been an increasing interest in designing compliant robots which exploit body dynamics for adaptive locomotion. It was shown that freevibration of elastic mechanical structures can generate energyefficient hopping/walking behavior. However, the velocity of such robots is very low. From this perspective, this paper presents a novel design strategy for running robots which makes use of torsional vibration of elastic beam. We propose a simple physical model which can be used to obtain the resonance frequency of the robot during stance phase. Moreover, this model can represent the dynamic behavior of such a robot during running locomotion.