An analysis has been made of the static elastic flaw of the structure by using the dual reciprocity boundary element method, with an exponential radial basis function adopted to interpolate and fit the physical force term. With the help of its special solution in elasticity and the dual reciprocity technique, the volume fraction in the original boundary integral equation is transformed into boundary integral, to be followed by an application of the boundary element discretization technology to the construction of the linear equations with the displacement and surface force on the boundary nodes as unknowns. Based on numerical examples, it is verified that the dual reciprocity boundary element method is an effective numerical calculation method for analyzing structural static elastic flaws, with its accuracy further verified by a comparison of the results with the finite element method software under actual working conditions. The example results show that the dual reciprocity boundary element method is characterized with a high accuracy in analyzing structural static elastic problems, applicable for a solution of the non-homogeneous problems with domain integral terms in other fields.