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This paper presents a sub-block algorithm for the time stepping finite element solution of problems in which sets of electromagnetic field equations, circuit equations and mechanical equation are coupled together. The proposed method ensures that identical solutions are obtained for the sub-blocks by controlling the step size of the time stepping process. This new method simplifies the process of dealing with coupled-system problems and it also greatly reduces the computation time. A time stepping finite element model of an induction motor is used to demonstrate the proposed method in details.