This work is concerned with numerical computational procedures required to determine the mechanical response (displacements, strains and stresses) in composites built up of sectors with both elastic and viscoelastic components, in isothermal conditions. We compare a proposed scheme: a Finite Element Method Only procedure (FEM-only), with a published scheme based on an integrated Boundary Element Method/Finite Element Method (BEM/FEM) scheme. In the former, all the constituents (elastic and viscoelastic) are given a finite element discretization; whereas in the latter, the constituents are given differentiated discretizations. A novel two tier homogenization is presented: a material mathematical treatment homogenization of the viscoelastic and elastic material properties is developed and implemented resulting in a significantly efficient computational procedure; and a Dirichlet homogeneous series representation (same number of terms and same relaxation times) for all materials considered is used as well. The proposed solution structure is not viscoelastic model specific and hence significantly more general. Both model data type and/or experimentally determined data are handled with ease either separately or simultaneously. The comparison is done on the basis of applying the stated FEM-only strategy to three benchmark type problems presented in the published reference. We show that the FEM-only scheme results match rather well the actual solutions of the three problems, requiring significantly lower mathematical formulating effort and concomitantly a lower programming work. Additionally, it is shown that the FEM-only procedure is general, robust, accurate and stable, requiring relatively small computational times when implemented in personal computers. Two novel benchmark type problems are proposed for which both the analytic solution and the numerical solution are included, in order to illustrate both the generality and the accuracy of the FEM-only proposed method.