The dual-primal finite element tearing and interconnecting (FETI-DP) method is combined with the Newton-Raphson method to expand the capability and improve the efficiency of three-dimensional finite element analysis (FEA) of nonlinear electromechanical and electric machine problems. Despite its modeling capability and high degree of accuracy, FEA has high computational complexity, especially for nonlinear analysis. The FETI-DP method is a robust domain decomposition method, which is a suitable choice for improving the efficiency of large-scale 3-D nonlinear FEA. The FETI-DP method decomposes the original large-scale problem into multiple subdomains, which can then be handled by parallel computing techniques so that the total computation time is reduced significantly. Linear and nonlinear regions are separated using the FETI-DP method. This further improves simulation efficiency and flexibility. Cubic splines and relaxation techniques are adopted to ensure stable and fast convergence of the Newton-Raphson method.