Based on a well-established nonincremental interaction law for fully anisotropic and compressible elastic-inelastic behavior of polycrystals, tangent formulation-based and simplified interaction laws, of softened nature, are derived to describe the nonlinear elastic-inelastic behavior of fcc polycrystals under different loading paths. Within the framework of small strain hypothesis, the elastic behavior, which is defined at granular level, is assumed to be isotropic, uniform, and compressible neglecting the grain rotation. The heterogeneous inelastic deformation is microscopically determined using the slip theory. In addition, the granular elastic behavior and its heterogeneous distribution from grain to grain within a polycrystal are taken into account. Comparisons between these two approaches show that the simplified one is more suitable to describe the overall responses of polycrystals notably under multiaxial loading paths. Nonlinear stress-strain behavior of polycrystals under complex loading, especially a cyclic one, is of particular interest in proposed modeling. The simplified model describes fairly well the yield surface evolution after a certain inelastic prestraining and the principle cyclic features such as Bauschinger effect, additional hardening, etc.