To determine the exact distribution of tensile stress in a cold rolled strip, tensile stress evolution caused by lateral uneven velocity distribution outside the deformation zone of the strip is examined. The finite difference method is employed to solve the problem. Different factors, including the strip width and the form and amplitude of the initial stress distribution on the stress evolution, are analyzed. On the one hand, to improve the calculation speed, a “Gaussian” curve is proposed to fit the results calculated by the finite difference method. Simulation results show that the stress evolution calculated by the fitting equation is in good agreement with that obtained by the finite difference method. On the other hand, to verify the exactness of the model, an experiment is conducted, and the comparison between the calculated results and experimental values is discussed.