In　order　to　accurately　and　efficiently　simulate　the　dynamic　processes　of　coupled　phenomena　with　viscoelastic,　continuous　and　discontinuous　deformations,　a　three-dimensional　(3D)　numerical　manifold　method　combining　Maxwell＇s　viscoelasticity　(3D-VisNMM)　is　proposed　and　implemented　in　this　study.　First,　the　matrix　formulas　of　3D-VisNMM　are　derived,　and　then　its　technique　flowchart　is　presented.　Second,　four　viscoelastic　models,　which　represent　creep　characteristics,　stress　relaxation　features,　stress　accumulation,　and　frictional　deceleration,　respectively,　are　used　to　verify　the　feasibility　of　3D-VisNMM.　The　creep　model　shows　that　the　simulated　deformation　at　each　time　step　is　highly　consistent　with　the　analytical　solution.　The　stress　relaxation　model　shows　that　the　accuracy　of　simulated　stress　mainly　depends　on　the　time　step,　that　is,　the　range　of　the　Relative　Standard　Deviation　(RSD)　is　0.3%-4.8%,　which　corresponds　to　a　time　length　of　0.1-2.0　years.　The　gravity-driven　stress　accumulation　model　shows　that　the　RSD　between　the　simulated　results　and　analytical　solutions　is　less　than　0.004%.　The　frictional　deceleration　simulation　shows　that　the　RSD　of　cumulative　displacements　and　accelerations　are　less　than　0.65%　and　2.4%,　respectively.　All　these　numerical　simulations　show　that　3D-VisNMM　is　suitable　for　analyzing　viscoelastic　deformations,　stress　relaxation,　and　frictional　sliding　issues　in　multitemporal　scale　(second-century)　and　multispatial　scale　(meter-hundred　kilometers).　Therefore,　3D-VisNMM　has　a　good　application　prospect　in　Geoscience　research.　©　2020　American　Society　of　Civil　Engineers.