Abstract: A nonlinear finite element based on the total Lagrangian incremental formulation of a two dimensional anisotropic medium is developed, and its application in the geometrical nonlinear buckling and postbuckling analysis of stiffened layered composite shell is demonstrated via example problems under the combination of mechanical loading and hygrothermal loading. The finite element based on the Sander's shell theory with transverse shear strains is also presented. The tangential stiffness matrices of rectangle shell finite element, the beam and curved beam, the equivalent hygrothermal force vector, and the method of analysis of buckling and postbuckling are given. Finally, several example problems are illustrated by the FORTRAN Programme.