Abstract The subject of this paper is the efficient and accurate determination of second-order design sensitivities in elastic bodies. The approach being carried out here is the direct differentiation of the governing derivative boundary element method (DBEM) formulation of the problem. Second-order sensitivities of boundary stresses are obtained here in an elegant manner. A numerical implementation of the method is carried out with isoparametric quadratic boundary elements and numerical results are presented for several sample problems. Considerable savings in computational effort for an optimization procedure is possible through the use of efficiently determined accurate second-order design sensitivities.