The nonlinear global-local analysis methods for the poling process of piezo-electoelastic materials, based on the mathematical homogenization method, are developed in this paper. The most of piezoelectoric ceramics are known to be polycrystalline structures in their micro-structure, in which each perovskite crystal or each domain has different direction of polarization. The macroscopic charging or loading switch the spontaneous polarizations in each crystalline structure, and this microscopic domain switch observed as hysteresis behavior or poling process from the macro-scale. In this study, the polycrystalline structures and switching phenomena are modeled as the microscopic structures in context of the multi-scale modeling, and the macroscopic nonlinear piezo-electoric properties affected by the microstructures are evaluated by using the homogenization method.