Abstract: This work focuses on the simulation of mechanical contact between nonlinearly elastic objects, such as the components of the human body. In traditional methods, contact forces are often defined as discontinuous functions of deformations, which leads to poor convergence characteristics and high-frequency noises. We introduce a novel penalty method for finite-element simulation based on the concept of material depth, which is the distance between a particle inside an object and the object's boundary. By linearly interpolating precomputed material depths at node points, contact forces can be analytically integrated over contact surfaces without raising the computational cost. The continuity achieved by this formulation reduces oscillation and artificial acceleration, resulting in a more reliable simulation algorithm.