We present an analytic solution for the deformation near an infinite strike-slip fault in an elastic layer overlying a linear viscoelastic half-space. The theory is valid for any linear viscoelastic rheology and any earthquake sequence. This is a generalization of the work of J. C. Savage and colleagues, which only holds for models with a uniform shear modulus, Maxwell viscoelastic lower half-space, and periodic rupture recurrence. We demonstrate the theory for models of an elastic layer over a Maxwell, standard linear solid, Burgers, and triviscous half-space. For each of these models, we calculate example postseismic displacements, interseismic displacements in a periodic earthquake sequence, and interseismic displacements for a nonperiodic earthquake sequence. Our solution is for a simple geometry; however, the model presents an elegant tool to explore the evolution of displacements for relatively complex rheologies and rupture recurrence histories.