A criterion for the occurrence of a reduction in the contact stress at the entrance to the deformation zone during the strip cold rolling is found. Numerical integration of the Karman equation determines the influence of friction conditions, tension and hardening of the strip material on the dimensions of this area. It is shown that neglecting the area of contact stress reduction and the shape of the hardening curve in the known solutions leads to an error in determining the rolling force, reaching 20% or more. A new solution of Karman’s equation is proposed, which significantly improves the accuracy of calculation of contact stresses and rolling forces by considering the area of contact stress reduction and shape of the hardening curve of the strip material.