For the problems of complex formulas and large amount of calculation faced by using simplex integration method to handle the high-order functions in manifold element integration, the Gaussian integration method was proposed to integrate manifold elements. Then, based on the numerical manifold method, a numerical simulation study was conducted on the process of metal plastic forming. Furthermore, for the upsetting of model, the right half of the axisymmetric geometric shape was taken for research, the finite cover system was established, the feature tracking points were set up at the intersection of free boundary and fixed mathematical grid, the initial velocity of tracking points were calculated, and the displacement coordinates of tracking points were obtained by multiplying the initial velocity by the time step to solve the key problem of accurate tracking for the plastic deformation free motion interface on the finite cover system and update the research method of manifold elements. By integrating the generated manifold elements and writing codes, a feasible algorithm is generated, which provides a new high-precision and high-efficiency numerical method for the computer simulation of metal plastic forming.