Earthquakes on intra-continental faults do not only cause immediate displacements and damage on the surface, but also induce sudden changes in pore fluid pressure as well as postseismic viscoelastic flow in the lower crust and lithospheric mantle. Such transient processes affect the velocity and stress field of the crust in the surrounding of the source fault for decades and cause significant Coulomb stress changes, which may trigger or delay next earthquakes on adjacent faults (receiver faults). The calculation of these stress changes has become an important tool for seismic hazard evaluation, but the combined influence of coseismic slip, interseismic stress accumulation and transient postseismic processes including poroelastic effects and viscoelastic relaxation on the velocity and stress field in the crust has not been systematically studied so far. 2D and 3D finite-element models with a generalized model setup are used to investigate the relative importance of the different earthquake-induced processes during the co- and postseismic phase of an intra-continental dip-slip earthquake. The models include gravity, isostatic effects, a regional stress field, elastic and viscoelastic layers and pore fluid pressure. In different experiments, important model parameters, including permeability, viscosity, friction coefficient, the size of the coseismic slip and the extension/shortening rate are varied to evaluate their influence on the model results. In the 2D models, a variation of the permeability of the crust and the viscosity of the lower crust and lithospheric mantle shows, that postseismic velocity fields contain signals from overlapping poroelastic and viscoelastic effects. Both processes may influence the velocity field already in the early postseismic phase, up to several decades, depending on the combination of upper-crustal permeability and lower-crustal viscosity. In the 3D models, the permeability of the crust and the viscosity of the lower crust and lithospheric mantle, as well as the friction coefficient, coseismic slip and deformation rate are varied, to evaluate their effect on the Coulomb stress changes on the receiver faults in the model fault array. While the latter three parameters have only an effect on the stress change magnitude, poroelastic effects and viscoelastic relaxation have a strong impact on the magnitudes and patterns of Coulomb stress changes. Poroelastic effects alter the coseismic Coulomb stress changes immediately in the first month after the earthquake, causing stress changes one order of magnitude stronger than those caused by viscoelastic relaxation. If the permeability and viscosity are low enough, the signals from both processes overlap already in the early postseismic phase for decades after the earthquake.