The dual-primal finite element tearing and interconnecting (FETI-DP) method is combined with the tree-cotree splitting (TCS) method to expand the capability and improve the efficiency of the finite-element analysis of electromechanical devices. With the FETI-DP method, an original large-scale problem is decomposed into smaller subdomain problems and parallel computing schemes are then employed to reduce the computation time significantly. The TCS method is adopted to deal with the low-frequency breakdown problem, which often accompanies the finite-element analysis of electromechanical problems. The proposed technique is applied to solve a multi-connected eddy-current problem and compute force for a magnetostatic problem. The results show that the proposed method can achieve an excellent accuracy and a good parallel efficiency.