The hybrid boundary node method (HBNM) is a promising method for solving boundary value problems with the hybrid displacement variational formulation and shape functions from the moving least squares(MLS) approximation. The main idea is to reduce the dimensionality of the former and keep the meshless advantage of the latter. Following its application in solving potential problems, it is further developed and numerically implemented for 2D solids in this paper. The rigid movement method is employed to solve the hyper-singular integrations. Numerical examples for some 2D solids have been given to show the characteristics. The computation results obtained by the present method are in excellent agreement with the analytical solution.The parameters that influence the performance of this method are studied through numerical examples.