Abstract: A geometrical nonlinear quasi-conforming nine-node quadrilateral degenerated shell element is constructed, based upon the nonlinear quasi-conforming finite element method. First, the geometrical description and displacement model of the nine-node quadrilateral degenerated shell element are given. Then, the nonlinear quasi-conforming finite element method is discussed and the assumptions for stress and strain are given. Last, the numerical calculations for a square plate, a circular arch, a spherical shell and two cylindrical shells are carried out with the constructed shell element. The results are compared with exact and other finite elements' solutions, which indicates that the shell element is accurate and efficient.

Key words: the quasi-conforming finite element, nonlinearity, plates, shells