In order to solve the problems that it is difficult to integrate the nonlinear Mises specific plastic power and that the corresponding total rolling power is hard to be calculated analytically, this paper establishes the expression of an linear specific plastic power to analyze the energy of the proposed elliptical velocity field and obtains an analytical solution of rolling force and energy parameters. In this paper, a new yield criterion linearly combined of principle stress components is established by calculating the integral mean value of the variable angle yield function. Its locus on the π-plane is a dodecagonal shape with equal sides and unequal angles, and its Lode parameter expression result was in good agreement with the experimental data. Meanwhile, according to the characteristic that the metal flow velocity increases gradually from the entrance to the exit of heavy plate, a velocity field whose horizontal velocity component satisfies the elliptic equation was proposed, which meets the kinematic admission condition. With the rolling energy analysis, the internal deformation power based on the proposed linear yield criterion, as well as the friction power and the shear power based on the strain vector internal product method were obtained. On this basis, the analytical solutions of rolling torque, rolling force, and stress state coefficient were obtained by the extreme variation of functional, which were compared with the measured data. Results show that the rolling torque and the rolling force obtained by using the yield criterion and the velocity field proposed in this paper were in good agreement with the measured values, where the rolling force error was less than 5.3% and the rolling torque error was about 6%.