Contact modeling plays a central role in motion planning, simulation and control of legged robots, as legged locomotion is realized through contact. The two prevailing approaches to model the contact consider rigid and compliant premise at interaction ports. Contrary to the dynamics model of legged systems with rigid contact (without impact) which is straightforward to develop, there is no consensus among researchers to employ a standard compliant contact model. Our main goal in this paper is to study the dynamics model structure of bipedal walking systems with rigid contact and a novel compliant contact model, and to present experimental validation of both models. For the model with rigid contact, after developing the model of the articulated bodies in flight phase without any contact with environment, we apply the holonomic constraints at contact points and develop a constrained dynamics model of the robot in both single and double support phases. For the model with compliant contact, we propose a novel nonlinear contact model and simulate motion of the robot using this model. In