By incorporating the constitutive framework of crystal plasticity into the multi-scale modeling based on the mathematical homogenization theory, we introduce the multi-scale analysis method for polycrystalline metals. The macroscopic material behavior of polycrystalline metals is characterized by the microscopic mechanical behavior affected by the shape and the chain axis of crystal grain, whereas the constitutive model for a single crystal is formulated by means of the multiplicative decomposition o the deformation gradient. Several numerical analyses are conducted to evaluate the macroscopic yield surfaceof a polycrystalline metal and examine the micro-scale inelastic behavior, which is very complex and inhomogeneous in the microstructure composed of several crystals.