Although structures made of functionally graded materials have been studied by many researchers, no research may be found in literature on boundary element analysis of the functionally graded viscoelastic structures. In the present paper, a 2D boundary element formulation capable of modeling time-dependent functionally graded materials (FGM) is presented. A numerical implementation of the Somigliana identity in terms of the displacements is developed to solve 2D problems of the exponentially graded viscoelasticity. The FGM concept can be applied to various materials, for structural and functional purposes. In this model, only Green functions of the nonhomogeneous elastostatic problems are needed with material properties that vary continuously along a given dimension. Results reveal that the boundary element approach can successfully be employed for the present complicated problem for arbitrary time histories of the applied loads and arbitrary boundary conditions, without the need to use relaxation functions or mathematical transformations.