Designers need advanced tools to tap the full potential of the benefits of giant magnetostrictive materials (GMMs) for advanced commercial, space, and military applications. To overcome the deficiencies in present models, a new magnetostrictive analytical formulation needs to be developed that includes the nonlinearities experienced in advanced device designs. Presented herein are a strategy and approach for developing the needed advanced tools to move magnetostrictive transducer design to much higher levels of performance and effectiveness. Advanced GMM FEM modeling capabilities are being developed by extending and combining leading edge theoretical work in nonlinear constitutive equations and ferromagnetic hysteresis. A nonlinear constitutive model for a GMMs uses a Taylor series expansion of independent variables of stress, magnetization and temperature to obtain a polynomial relation in terms of the Gibbs free energy. Phenomenological justification is used to eliminate some terms. Development of a magnetization based magnetostrictive material model at the macroscopic continuum level will be a novel advancement of the state of the art. The planned hysteresis model is derived from related work on energy-based models which considers the total magnetization as the combination of a reversible and an irreversible component. Because both the constitutive and hysteresis formulations are in terms of the same state variables, integration into a new complete magnetostrictive material description is inherently more feasible. The result will be a validated, fully coupled, 3-dimensional, nonlinear, hysteretic, dynamic thermo-electro- magneto-acousto-mechanical (TEMAM) model of magnetostrictive materials. Development of new finite elements to take advantage of the advanced modeling results is planned. The new capability will provide meaningful performance predictions, parameter sensitivity studies, trade-off studies and design optimizations, thereby enabling next-generation applications at reduced developmental cost.