Closed-form formulations are difficult to find when the material behavior law is nonlinear. A linear approximation, on the other hand, has a very narrow range of validity. In this communication, the Normal Form (NF) method is employed to solve a 1-D nonlinear magnetodynamic problem. The discrete model is formulated in a state-space form suitable for NF applications. The resulting system is then expanded on a linear mode basis to cubic order. Analytical solutions are obtained using the NF technique and compared to traditional solutions. The results show the cubic polynomial adequately approximates the problem, and the NF solution is valid for some range of magnetic field intensity.