Postseismic surface deformations are attributed to the inelastic flow of the subcrustal regions of the earth following an earthquake. A multilayer representation of the earth's rheological properties is used in conjunction with a finite element computational scheme to calculate time-dependent displacements and strains subsequent to a strike-slip earthquake. The deviatoric stress-strain relation for the uppermost layer is assumed elastic. Lower layers are assumed to be, in order of increasing depth, a standard linear, three-element, viscoelastic solid; a linear viscoelastic fluid; and another elastic solid. Physically these layers correspond to the upper lithosphere, lower lithosphere, asthenosphere, and lower mantle, respectively. Elastic dilational properties are assumed throughout. Appreciable postseismic displacements, possibly approaching meters for large earthquakes, arise from the viscoelastic relaxation following the sudden coseismic slip. Furthermore, compared to the simpler case of an elastic lithosphere over a viscoelastic asthenosphere the near-fault postseismic shear strain is increased, by a factor of two or more in some cases, by the presence of a viscoelastic lower lithosphere. Also the duration of postseismic straining is increased if the viscosity of the lower lithosphere is greater than that of the underlying asthenosphere.