Unfaulting seismic images to correlate seismic reflectors across faults is helpful in seismic interpretation and is useful for seismic horizon extraction. Methods for unfaulting typically assume that fault geometries need not change during unfaulting. However, for seismic images containing multiple faults and, especially, intersecting faults, this assumption often results in unnecessary distortions in unfaulted images. We have developed two methods to compute vector shifts that simultaneously move fault blocks and the faults themselves to obtain an unfaulted image with minimal distortions. For both methods, we have used estimated fault positions and slip vectors to construct unfaulting equations for image samples alongside faults, and we have constructed simple partial differential equations for samples away from faults. We have solved these two different kinds of equations simultaneously to compute unfaulting vector shifts that are continuous everywhere except at faults. We have tested both methods on a synthetic seismic image containing normal, reverse, and intersecting faults. We also have applied one of the methods to a real 3D seismic image complicated by numerous intersecting faults.