Abstract: A triangular or rectangular element was used for the numerical computation in a general numerical manifold method (NMM). For many practical problems, a polygonal element can adjust to the complicated configuration of a computational domain easily, hence a polygonal manifold element is analyzed for numerical computation. The convex polygonal mesh for a manifold element is constructed based on a Delaunay triangulation mesh. An improved Wachspress shape function is used as a weight function of the numerical manifold method. The validity of the proposed numerical manifold method is illustrated by the analysis of a thin plate bending problem. Numerical manifold formulas and element matrices are also derived for the numerical example. The results show that this method, compared with the finite element method, can improve accuracy and convergence greatly.