Using models of infinite length strike-slip faults in an elastic layer above linear viscoelastic regions, we investigate interseismic deformation. In the models we investigate, interseismic strain accumulation on mature faults is the result of the cumulative effects of all previous ruptures and is independent of the fault loading conditions. The time for a fault to spin-up to a mature state depends on the rheologies and the fault loading conditions. After the model has spun-up, the temporal variation of shear stresses is determined by the fault slip rate and model rheologies. The change in stress during spin-up depends on the slip rate, rheologies, and fault loading conditions but is independent of the magnitude of the initial stress. Over enough cycles such that the cumulative deformation is block-like, the average mature interseismic velocities are equal to the interseismic velocities of an elastic model with the same geometry and distribution of shear moduli. In a model that has spun-up with the fault rupturing periodically, the cumulative deformation is block-like at the end of each seismic cycle, and the interseismic deformation is cycle-invariant (i.e., the same in all cycles). When the fault ruptures nonperiodically, the fault spins up to a mature state that is the same as if the fault had ruptured periodically with the mean slip rate. When the fault slip rate within each cycle varies, the interseismic deformation evolves toward the cycle-invariant deformation determined by the most recent fault slip rate. Around a fault whose slip rate has been faster (slower) than average, interseismic velocities are larger (smaller) than the cycle-invariant velocities and increase (decrease) from cycle to cycle.