According to the dynamic Coulomb wedge model, coseismic strengthening of the shallowest part of the subduction interface can cause permanent deformation of the overlying outer wedge, so that the cumulative effects of great interplate earthquakes control the geometry of the wedge. In this work, we use a numerical model, which is a hybrid of the frictional contact model and the classical crack model, to study how stress is coseismically transferred from the seismogenic zone to the strengthening updip zone to cause wedge deformation. In this static model, the “critical strengthening” required to prevent the rupture from breaking the trench depends on the force drop of the seismogenic zone, defined as the product of the average shear stress drop and the area of the seismogenic zone. In a simple model of uniform material properties with a few megapascals average stress drop over a seismogenic zone of 120 km downdip width, the critical strengthening for a 30 km wide updip zone is an increase in the effective friction coefficient by about 0.05. Using the Coulomb wedge theory, we demonstrate that this level of strengthening can readily push the overlying wedge into a critical state of failure. With much greater strengthening, the rupture is able to extend into the updip zone only slightly, causing localized wedge compression in the area of slip termination. We examined wedge geometry of 22 subduction zones in the light of the model results. We found that the surface slope of these wedges is generally too high to be explained using the classical wedge theory but can be explained using the dynamic Coulomb wedge model including coseismic strengthening of the shallow portion of the megathrust.