In this study, calendering process of an Oldroyd 4-constant model with the non-linear slip condition is presented. The fundamental laws are used to formulate the flow equations and then are simplified under lubrication approximation theory. We introduced the stream function to eradicate the pressure gradient and then numerically solved the final equations using the "bvp4c method" to determine the stream function and velocity profiles. The pressure gradient, pressure, and mechanical quantities of calendering operations are computed using the Runge-Kutta 4th-order approach. Using a variety of graphs, it is discussed how the slip, Hartmann number, and material parameters of an Oldroyd 4-constant fluid affect the velocity, pressure gradient, and other associated characteristics of calendering. The results reveal that on comparing to the no-slip situation, the pressure distribution inside the calender and the length of contact decreases with increasing slip parameter values. On the other hand, the Hartmann number is responsible to enhance pressure. Furthermore, a reduction is observed in final sheet thickness with increases the values of the slip parameter (Kn). The force, and power are the decreasing function of α1, conversely, these quantities increase with enhancing the values of exit points.