<p>There are many studies on polygonal mesh generation in which the technology is not difficult in theory. But for the complex geometric shapes, the processing of elements on boundary is relatively complex, and there are some difficulties in program implementation. In addition, the original polygonal FEM have many shortcomings such as complex derivation operations of rational polynomial shape functions, a reduced accuracy or slow convergence and even failure for isoparametric distorted elements. In this work, the 2D mesh generation for arbitrary polygonal elements is firstly realized by using Python programming, in which the quality of the initial polygonal meshes is greatly improved by Centroidal Voronoi Tessellation(CVT) and some algorithms for deleting short edges and sorting counterclockwise are proposed. The object-oriented cell-based S-FEM for polygonal elements (<i>n</i>CS-FEM) is then proposed to find the solution of elastic–plastic problems. Polygonal elements are thus allowed to be of arbitrary shape, which can avoid the distortional elements and reduce the limitation for mesh quality. The effectiveness and mesh adaptability of <i>n</i>CS-FEM have been verified by applying the resulting polygonal meshes and <i>n</i>CS-FEM models to the solution of elastic–plastic problems. Combined with the object-oriented programming methods, it can greatly shorten the development cycle and reduce the development difficulty of <i>n</i>CS-FEM programs.</p>