In the paper,a hybrid polygonal element based on anisotropic Greens functions was developed for solving fully anisotropic elastic materials.In the present hybrid element,the interior displacement and stress fields were approximated by the linear combination of anisotropic Greens functions derived by Lekhnitskii formulation,the element frame fields were constructed by the interpolation of general shape functions widely used in the conventional finite element,and then they are linked by a new double-variable hybrid functional.Because the approximated interior fields exactly satisfied the anisotropic elastic governing equations,all integrals in the present hybrid functional were performed along the element boundary so that arbitrary hybrid n-sided convex polygonal element can be constructed for practical use and corresponding displacement and stress fields everywhere in the element can be evaluated accurately.Finally,the present hybrid element was verified by making comparison of numerical results or exact solutions in a cantilever composite beam and an infinite composite plate containing a circular hole,which are all made with angled lamina.