The compass-gait biped model is a unique, yet simple model, often used as a test bench for new control strategies in the field of legged locomotion. This paper presents a novel continuous mathematical model for compass-gait biped robots, modeling the discontinuities in impact with a nonlinear function. Natural oscillation is defined as a free response under the damping compensation to achieve persistent oscillation. The phenomenon of natural oscillation was previously exploited in the linear dynamics of multi-segmental locomotor, and it is now extended to this humanoid system with the contact force from the ground modelled with a nonlinear bump function.