The pertinent translation rule is proposed for the elastic-core, i.e. similarity-center of the sub-loading surface to the normal-yield surface in addition to the generalization of nonlinear anisotropic hardening rule. Incorporating them, the subloading surface model formulation is refined for the hypoelastic-based plasticity and the hyperelatic-based plasticity with the multiplicative decomposition of deformation gradient. The plastic spin and the dissipative spins of the anisotropic hardening variables are also formulated rigorously based on them.