In nonproportional loading process, the traditional elastoplasticonstitutive model predicts the unrealistically stiff mechanical response leading to an excessively high critical load. The new concept of the tangential stress rate relaxation, called the tangential relaxation, is proposed by Hashiguchi, in which the direction of the tangential strain rate induced by the tangential stress rate has the components not only tangential but also outward-normal to the subloading surface. In this paper, the validity of the concept for the prediction of the deformation behavior of sand is evaluated by simulating the directional dependency of the inelastic strain increment on the stress increment directions, i.e. vertex effect, and also the inelastic deformation during the rotation of the principal stress axes direction under the constant mean stress and deviatoric stress, i. e. non-coaxiality.