Geodetic data and field observations demonstrate that the emplacement of dikes in volcanic rift zones frequently generates normal faulting and graben subsidence at the Earth's surface. Elastic modeling of the vertical ground-surface displacements above dikes and faults indicates that the extent of graben subsidence can be achieved only if fault slip extends virtually to or beyond the dike plane at depth. A mechanical model that includes dikes and frictional faults shows that dike opening tends to compress and lock faults located to either side of the dike. Therefore, slip extending into or beyond the dike cavity must occur either (1) on faults that intersect the dike near its top, above the zone of dike-induced compression, or (2) on faults that slip ahead of the dike as it propagates laterally. Data from Iceland indicate that slip occurred on deep faults that presumably slipped in advance of the laterally propagating dike.