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Earthquakes in the brittle upper crust induce viscoelastic flow in the lower crust and lithospheric mantle, which can persist for decades and lead to significant Coulomb stress changes on receiver faults located in the surrounding of the source fault. As most previous studies calculated the Coulomb stress changes for a specific earthquake in nature, a general investigation of postseismic Coulomb stress changes independent of local geological conditions is still lacking for intra-continental dip-slip faults. Here we use finite-element models with normal and thrust fault arrays, respectively, to show that postseismic viscoelastic flow considerably modifies the original coseismic Coulomb stress patterns through space and time. Depending on the position of the receiver fault relative to the source fault, areas with negative coseismic stress changes may exhibit positive postseismic stress changes and vice versa. The lower the viscosity of the lower crust or lithospheric mantle, the more pronounced are the transient stress changes in the 1st years, with the lowest viscosity having the largest effect on the stress changes. The evolution of postseismic Coulomb stress changes is further controlled by the superposition of transient stress changes caused by viscoelastic relaxation (leading to stress increase or decrease) and the interseismic strain accumulation (leading to a stress increase). Stress changes induced by viscoelastic relaxation can outweigh the interseismic stress increase such that negative Coulomb stress changes can persist for decades. On some faults, postseismic relaxation and interseismic strain accumulation can act in concert to enhance already positive Coulomb stress changes. © 2017, Springer-Verlag Berlin Heidelberg.