A numerical implementation of the Somigliana identity in displacements for the solution of 3D elastic problems in exponentially graded isotropic solids is presented. An expression for the fundamental solution in displacements, U jℓ, was deduced by Martin et al. (Proc. R. Soc. Lond. A, 458, pp. 1931-1947, 2002). This expression was recently corrected and implemented in a Galerkin indirect 3D BEM code by Criado et al. (Int. J. Numer. Meth. Engng., 2008). Starting from this expression of Ujℓ, a new expression for the fundamental solution in tractions Tjℓ has been deduced in the present work. These quite complex expressions of the integral kernels U jℓ and Tjℓ have been implemented in a collocational direct 3D BEM code. The numerical results obtained for 3D problems with known analytic solutions verify that the new expression for T jℓ is correct. Excellent accuracy is obtained with very coarse boundary element meshes, even for a relatively high grading of elastic properties considered. Copyright © 2007 Tech Science Press.