In　this　research,　the　dynamic　features　of　three-directional　functionally　graded　materials　(3DFGMs)　rectangular　parallelepiped　with　classic/elastic　restraints　are　investigated　based　on　3D　elastic　theory.　The　general　boundary　conditions　are　implemented　by　introducing　artificial　displacement　springs　on　the　chosen　surfaces　of　rectangular　solid.　The　gradient　materials　are　distributed　along　the　two　in-plane　and　thickness　directions　of　parallelepiped.　By　setting　boundary　constraints　and　geometric　parameters,　the　3DFGMs　rectangular　parallelepiped　can　be　evolved　into　slender　beam,　thick　or　thin　plate,　or　even　a　cuboidal　solid.　Lagrangian　energy　functions　are　formulated　for　parallelepiped-spring　system.　The　free　vibration　characters　of　3DFGMs　rectangular　parallelepiped　are　solved　employing　the　Ritz　method　in　conjunction　with　the　Jacobi　polynomials.　For　transient　analysis,　the　analytical　expressions　of　impulse　responses　are　derived　for　different　types　of　pulsed　excitation.　The　presented　modeling　and　solution　methods　are　validated　by　comparing　with　the　results　from　open　literature,　finite　element　analysis　and　experimental　results.　Numerical　simulations　are　performed　to　reveal　the　effect　mechanisms　of　material　gradients,　geometrical　configuration　and　boundary　restraints　on　the　vibration　characters　of　3DFGMs　parallelepiped.　The　results　demonstrate　that　dynamic　performance　of　rectangular　parallelepiped　depends　critically　on　material　gradient　which　may　be　regarded　as　regulatory　factor　to　regulate　the　modal　displacement　distribution　or　modal　sequence.　©　2025　Elsevier　Ltd