The Ishtar Terra region contains the highest topography known on Venus, over 10 km above mean planetary radius, as well as abundant tectonic features, many of apparently compressional origin. These characteristics suggest that Ishtar is a crustal convergence zone overlying downwelling mantle. In order to explore quantitatively the implications of this hypothesis for Ishtar's origin, we present models of viscous crustal flow driven by gradients in topography. Assuming a free-slip surface boundary condition, we find that if the crustal convergence hypothesis is correct, then the crustal thickness in the plains surrounding Ishtar can be no more than about 25 km thick. This upper bound assumes a cold (10 K km-1) geotherm and the stiffest available diabase flow law. If the geothermal gradient is larger or the rheology is weaker, the crust must be even thinner for net crustal convergence to be possible. This upper bound is in good agreement with several independent estimates of crustal thickness of 15--30 km in the plains of Venus based on modeling of the spacing of tectonic features and of impact crater relaxation. If the surface layer of Venus provides a no-slip boundary, then our models allow the crustal thickness in the plains to be up to 50 km, but the likely existence of faults that cut through the crust makes a no-slip surface layer unlikely. Our upper bound on crustal thickness is much less than that derived from an airy isostasy model of Ishtar's gravity anomaly. Much of the observed gravity anomaly must be due to density anomalies in the mantle beneath Ishtar. Although we treat Ishtar as a crustal convergence zone, our crustal flow model shows that under some circumstances near-surface material may actually flow away from Ishtar, providing a possible explanation for grabenlike structures in Fortuna Tessera. ¿ American Geophysical Union 1991