A new, accurate, and efficient algorithm is developed for the numerical evaluation of a class of singular integrals which arise in the BEM (boundary element method) analyses. The algorithm is based on an idea of scaling integration that utilizes a proportional relationship inherent in the numerical computation of the singular integrals over flat triangular elements. The present algorithm (scaling integration method) avoids the direct numerical evaluation of the integrand in the neighborhood of singularities. It is shown and demonstrated that the method is simpler, faster, and more accurate than standard Gaussian integration algorithms. An application of the method to the BEM analysis is also described and the results are favorably compared with the exact solution. © 1989.