Thirty horizontal displacement time series from GPS sites in the area around the 2005 Kashmir earthquake show lateral spatial variations in displacement magnitude and relaxation time for the postseismic interval from 2005 to 2012. The observed spatial pattern of surface displacements can only be reproduced by finite element models of postseismic deformation in elastic over viscoelastic crust that include lateral differences in both the thickness of the elastic layer and the viscosity of the viscoelastic layer. Solutions reproducing the sign of horizontal displacements everywhere in the epicentral region also require afterslip on the portion of the fault dislocation in the viscoelastic layer but not in the elastic lid. Although there are substantial tradeoffs among contributions to postseismic displacements of the surface, the observations preclude both crustal homogeneity and shallow afterslip. In the best family of solutions, the thickness of the elastic upper crust differs by a factor of 5 and the viscosity of the middle and lower crust by an order of magnitude between domains north and south of a suture zone containing the Main Boundary Thrust and Main Mantle Thrust. Postseismic deformation in Kashmir varies laterallyCrustal sutures have mechanical implicationsMaterial heterogeneity can look like blind afterslip