The aim of this work is to discuss a new non linear intermediate model for large viscoplastic deformations that could predict the texture transition and stress-strain behavior in a range that spans from the upper bound (Taylor) to the lower bound (Sachs or static) estimates. In this model, we introduced a single parameter, f , as a weight function to formulate the proposed intermediate approach which combines the Taylor and Sachs estimates. This formulation leads to an interaction law by the minimization of a tensorial function which depends on the parameter f . For the applications, we focus on the uniaxial tension test. The results for texture evolution in an FCC polycrystal show that a transition between the copper type and brass type textures can be obtained by the proposed non-linear intermediate model.