In the world industry plant, solid and solid metals are always in contact even their motions not independent. Modeling of rolling die contact with slab primarily needs to describe the Tribology of contact phenomena. Consideration of continuum theory of rolling contact how a contact region is formed between rolling die and slab, and how the tangential force is distributed over the contact area with coefficient of friction is important. The central concern of numerical model is used in this work to indicate a set of equations, derived from the contact principle, that transfer the physical event into the mathematical equations including the laws of nature, such as newton’s laws, boundary conditions, state of stresses and their derivatives at particular time and locations. In this paper the elasticity stress behavior of rolling die contact with slab for number of cyclic loads is modeled. The model is including new proposed constitutive equations for discontinuity of the velocity, pressure distribution in rolling contact from the enter side to exit side of the neutral point. To verify the model, finite element simulation and experimental data from the literature are considered. The results show good agreement with finite element simulation and experimental data.