AbstractThe main goal of this paper is to bring forward and explore the issue of constitutive integrations in large deformation regime for anisotropic hyperelasto‐plastic material models. Of particular interest is the appropriate treatment of cases with non‐coaxiality of principal stress and its conjugate hyperelastic strain. The non‐coaxiality can result from hyperelastic anisotropy, anisotropic flow directions or anisotropic yield function. In addition to discussing issues related to non‐coaxiality, a constitutive integration algorithm is presented in some detail that is designed to be applicable to anisotropic non‐coaxial (as well as to isotropic) hyperelastic–plastic solids. A numerical example is used to illustrate the problem. Copyright © 2008 John Wiley & Sons, Ltd.