Vertical rolling is an important technique to control the width of continuous casting slab in hot rolling field. Accurate prediction of vertical rolling force is a core point to maintain rolling mill equipment. Due to the limitation of the algorithm, the prediction accuracy of most vertical rolling force models based on the energy method can only reach more than 10%. Therefore, it is challenging to optimize the rolling force model to improve the prediction accuracy. This paper presents an innovative approach for optimizing the calculation of vertical rolling force with a unified yield criterion. Firstly, the maximal width of dog bone region is determined by the slip-line method and described the dog bone shape via sine function model. Furthermore, proposed velocity and corresponding strain rate fields satisfy kinematically admissible condition is used to calculate the total power. Finally, the analytical solution of the rolling force and dog bone shape model is obtained by repeatedly optimizing the weighted coefficient b of intermediate principal shear stress on the yield criterion. And the effectiveness of the proposed mechanical model is verified by measured data in strip hot rolling field and other models’ results. The results shows that the prediction accuracy of vertical rolling force model can be improved by optimizing the value of b. Then, the impacts of reduction rate, initial thickness and friction factor on dog-bone shape size and vertical rolling force are discussed.