Abstract: Due to some confusions existing in the current coordinate description of large rotation and large strain of continuum mechanics, there are always undiscernible mistakes in the formulation of finite element method for large displacement problems. The object of this paper is to scrutinize some basic theoretical point of views in continuum mechanics of finite deformation by the author's geometrical field theory^[1][2], and to formulate fundamental equations of incremental displacement for finite element method by the energy principle of power type. The method described was used by Y. Shang^[9] and H. P. Xie^[10]. They obtained results which are in very good agreement with experiments of large deformation.

Key words: nonlinear physical model, ansatz method, analytical solution