Global Positioning System measurements across the east central Ventura basin, Transverse Ranges, southern California, before the nearby 1994 Northridge earthquake show high strain rates. Interpreting this rapid strain accumulation using the usual model of deep slip on a dislocation in a uniform elastic half-space requires slip to extend to within 5 km of the surface. Such shallow slip is difficult to reconcile with the substantial coseismic displacement at depths from 7 to 19 km during the Northridge earthquake. Here we model the displacement and velocity fields throughout the earthquake cycle using a two-dimensional finite element model with a viscoelastic rheology. Displacements are driven by far-field and basal velocity boundary conditions and by imposed periodic earthquakes on the thrust faults bounding the basin. The thrust faults rupture through an elastic upper crust to a depth of 15 km. After a transient stage, during which stresses and strains build up to quasi-equilibrium values, the behavior of the model becomes periodic. The sum of the coseismic displacement divided by the repeat interval, plus the average interseismic velocity, is equal to the geologic velocity. The temporal variation in surface velocity depends mainly on the Elsasser relaxation time (proportional to the product of the Maxwell time of the lower crust and the ratio of the thicknesses of the entire crust and viscoelastic lower crust). We are able to match the observed high strain rate only if we include the observed variations in elastic modulus associated with the deep basin sediments. The model reconciles geologic, geodetic, and seismological observations of deformation. There are trade-offs among the far-field convergence rate, the Elsasser time, the earthquake repeat time, and the time into the earthquake cycle. Acceptable convergence rates range from 8 mm/yr, for a relaxation time of the lower crust of 300 years, to 12 mm/yr, for a 30-year relaxation time. ¿ 1999 American Geophysical Union