Abstract: The DN-Brent algorithm, a combination of damped Newton algorithm, which is based on the step-down idea for searching the damping factor in the Newtonian iterative direction, and one-dimensional Brent algorithm, which is based on the parabola interpolation idea, is employed in the rigid plastic finite element method to calculate rolling forces. Compared with the traditional Newton-Raphson (N-R) method, the computational results demonstrate that the rolling force values obtained by the two algorithms are both close to the practical measured values. However, the proposed algorithm needs less iteration numbers and CPU time, which verifies the accuracy and validity of the DN-Brent algorithm in the application of the rigid-plastic finite element method to the calculation of rolling forces.