In this paper, we present the role of ground contact angle in passive dynamic walking and running with analysis by two limb models from an energetic view. First, a massless limb model is proposed which introduces locomotion cost of running as a function of speed, limb length, ground contact angle and excursion angle. Furthermore, a mass-added limb model is created taking the limb mass into account during walking and running to estimate the energetic cost of limb swing. Our models indicate that ground contact angle is relevant to the force production which is necessary to swing the limb. To estimate the importance of ground contact angle in bipedal locomotion during walking and running, we create a bipedal robot with the wheel chair pushing task. Only one motor is used to drive each limb to perform two dimensional movements. Passive movements of the foot and knee rely on gravity and on the elasticity of springs on the limbs. The relationship between ground contact angle and energetic cost in bipedal locomotion is justified by experiments in different gaits.