A stable and efficient numerical scheme for the evaluation of surface integrals with 1/R-3-type singularities is presented. The method is based on the combination of the direct evaluation method and the singularity subtraction technique. The proposed method allows robust numerical evaluation of integral operators containing hyper-singular double normal derivative kernels in the cases where the integral equations are discretized with Galerkin's type techniques. (C) 2012 Elsevier Ltd. All rights reserved.