In　this　contribution,　the　three-dimensional　(3D)　finite-volume　direct　averaging　micromechanics　(FVDAM)　is　reconstructed　by　incorporating　parametric　mapping　capability　into　the　theory＇s　analytical　framework,　which　allows　using　arbitrarily　shaped　and　oriented　hexahedral　subvolumes　in　the　material　microstructure　discretization.　The　technique　is　then　further　extended　to　include　linear　viscoelastic　capability　to　investigate　the　creep　and　relaxation　behavior　of　polymeric　matrix　composites　and　stress　field　evolution　with　either　continuous　or　discontinuous　reinforcements.　Elastic-viscoelastic　correspondence　principle　is　employed　in　the　unit　cell　solution　to　relate　the　governing　relations　between　time　domain　and　Laplace-Carson　domain.　After　establishing　the　homogenized　constitutive　equations　and　solving　the　boundary　value　problems　in　Laplace-Carson　domain,　Zakian　inversion　scheme　is　used　to　invert　the　inexplicit　homogenization　functions　to　obtain　both　relaxation　moduli　and　stress　distributions　during　a　relaxation　history　in　real　space.　The　FVDAM　theory　via　correspondence　principle　is　validated　extensively　by　comparing　with　Mori-Tanaka,　finite-element,　locally　exact　solutions　and　experimental　data.　Good　agreement　between　the　present　theory　and　other　methods,　along　with　a　few　numerical　investigations,　explains　not　only　the　accuracy　of　the　3D　parametric　FVDAM　but　also　the　validity　and　efficiency　of　the　correspondence　principle　and　Zakian　inversion　technique.