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This paper studies different iterative solution methods for nonlinear permeance network based machine models. A new transmission line modeling (TLM) algorithm for efficient solution of permeance network models (PNM) of induction machines is proposed. In this method, the TLM algorithm is used to decouple the nonlinear magnetic equations. The decoupled nonlinear equations are then solved by a look-up table method owing to the repetitive nature of equations across the geometry of the machine. It is shown that the proposed method offers significant speed-up compared to the conventional Newton-Raphson method. Simulation results for dynamic and steady-state conditions of a closed rotor slot induction motor are compared with experimental test results as well as finite element analysis to evaluate the performance of the proposed algorithm.