Summary. The crustal deformation patterns associated with the earthquake cycle can depend strongly on the rheological properties of subcrustal material. Substantial deviations from the simple patterns for a uniformly elastic earth are expected when viscoelastic flow of subcrustal material is considered. The detailed description of the deformation pattern and in particular the surface displacements, displacement rates, strains, and strain rates depend on the structure and geométry of the material near the seismogenic zone. In the past few years various viscoelastic models of crustal deformation have been published. These models differ in their predictions concerning the temporal and spatial patterns of crustal deformation. In some cases these differences are due to varying choices for the physical mechanism under study. In other cases, however, the differences are the result of the details of the mathematical treatment or the choice of model paraméters. We seek to resolve the origin of some of these differences by analysing several different linear viscoelastic models with a common finite element computational technique. The models involve strike-slip faulting and include a thin channel asthenosphere model, a model with a varying thickness lithosphere, and a model with a viscoelastic inclusion below the brittle slip plane. The calculations reveal that the surface deformation pattern is most sensitive to the rheology of the material that lies below the slip plane in a volume whose extent is a few times the fault depth. If this material is viscoelastic, the surface deformation pattern resembles that of an elastic layer lying over a viscoelastic half-space. When the thickness or breadth of the viscoelastic material is less than a few times the fault depth, then the surface deformation pattern is altered and geodetic measurements are potentially useful for studying the details of subsurface geométry and structure. Distinguishing among the various models in best accomplished by making geodetic measurements not only near the fault but out to distances equal to several times the fault depth. This is where the model differences are greatest; these differences will be most readily detected shortly after an earthquake when viscoelastic effects are most pronounced. For a thin channel asthenosphere model we have found that the predicted displacements are less than those for a half-space asthenosphere. This result is contrary to recently published results based on analytical approximations. The deficiencies of the latter work result from ignoring material below the asthenosphere and in using thickness averaged deformation paraméters. Although the displacements predicted for a thin channel asthenosphere are less than those for a half-space asthenosphere, the post-seismic strain rates at intermediate distances from the fault are greater (in an absolute value sense) in the former model.