This work aims at introducing the concept of the numerical Green’s function (NGF) idea for elastostatic fracture mechanics using the boundary element-free method (BEFM). Unlike the local boundary integral equation method (LBIE), the BEFM only requires boundary interpolation. This method derives from the coupling of the boundary integral equation method and the orthogonal moving least-squares approximation scheme (OMLS). OMLS differs from standard MLS by using an orthogonal basis instead of only a linear independent one, which increases its accuracy and efficiency. Some illustrative examples are included in the end.