The traditional numerical manifold method (NMM) adopts the form of regional integration. This paper proposed a new NMM in the form of boundary integral by integrating the advantages of both the boundary element method (BEM) and the NMM, namely the dimension reduction of BEM and the flexibility of local base selection of NMM. For two-dimensional elastostatics problems, three different benchmark examples with analytical solutions are applied to verify the validity and efficiency of the newly proposed NMM. The results show that the accuracy of the proposed procedure can be effectively improved by increasing the order of the local basis.