In this research, a combination of the numerical manifold method (NMM) and boundary element method (BEM) is presented for solving plane elasticity problems to benefit from the advantages of both methods. For this goal, the domain of the problems is divided into two regions, each region is analyzed separately, and finally, equilibrium and compatibility conditions are controlled in the interface by the iteration method. 1D quadratic boundary elements and 2D quadratic, cubic and quartic ones in the form of triangular shapes are utilized in the boundary element and manifold methods, respectively. The proposed method is verified by calculating the displacements and stresses resulting from the application of static loads in five different numerical problems. Comparison of the numerical results shows that the suggested method is very efficient and accurate.