Abstract: Based on Total Lagrange Description method, GSQ24 shell element with in-plane drilling degrees of freedom is used in the geometrically nonlinear analysis of plate and shell structures. Under von Karman抯 assumptions of large deflections and small strains, the shear strains are accounted for. FEM formulae of the small displacement stiffness matrix, the geometric stiffness matrix and the initially displacement stiffness matrix have been established for large deflections of plate and shell structures. In the meantime, FEM formulae accounting for material and geometrical nonlinearity are developed in this paper. Compared with the results of variational method and series solution, the numerical results demonstrate the feasibility of the present method.