Abstract: In this paper, a new concept of subregion function method is suggested. According to the boundary shape and the stiffness and loading conditions of the structure, the original zone of the structure is divided into some subregions, in each of which different trial functions may be adopted. Conditions of compatibilities between subregioni are considered. Finally residual equations consisted of interior residuals, boundary residuals and co-boundary residuals between subregions are given.A numerical example to illustrate the theory of this method is given.

Key words: transversely isotropic, hyper-elastic material, rectangular plate with voids, finite deformation, potential energy principle, growth of voids