In this paper, a set of inelastic constitutive equations of poly-crystalline metals is derived by combining finite deformation kinematics of a single crystal component and the shear stress-shear strain relation of a slip system based on a thermo-activated motions of dislocations. The interactions among grains are incorporated by ″deformation gradient constant assumption″. The equations are rather simple internal variable theory type. By using these equations, some fundamental effects of grain rotations on the inelastic behaviors of polycrystalline metals in a finite deformation range are clarified under complex loading and elevated temperature conditions. Some comments are made on the problem of plastic spin tensor.