The volcanic rift zone in Iceland is characterized by elongate volcanic systems, consisting of tension fractures, normal faults and volcanic fissures, where most of the volcanotectonic activity takes place. Most volcanic systems develop central volcanoes, the formation of which is still poorly understood. There is great difference in the eruption and intrusion statistics of the volcanic systems inside and outside the central volcanoes. In the central volcanoes, eruptions are frequent (typically one every several hundred years), of small volume (normally less than 0.1 km3) and fed mainly by thin (average thickness of 0.5 m), inclined sheets. Outside central volcanoes the eruptions are rare (typically one every several thousand years) but of large volume (typically more than 1 km3) and fed mainly by thick (average thickness of 4--5 m), subvertical dikes. Using the results of a boundary element study of magma chambers modeled as a cavities or holes in a semi-infinite plate, these empirical relations, as well as the formation of specific central volcanoes in the volcanic systems, can be explained. Once a cavity-like magma chamber has formed, its existence in the rift zone concentrates tensile stress. This stress concentration causes the segment containing the magma chamber to rupture much more frequently than the other parts of the volcanic system, which partly explains the formation of central volcanoes and their high eruption frequencies. This concentration also gives rise to a local stress field that encourages injection of small-volume sheets in all directions and at various dips from their source magma chamber. The magma chamber acts as a trap for upward propagating dikes from mantle reservoirs and channels magma, through inclined sheets, toward a limited area at the surface where the central volcano gradually forms. The inverse relationship between eruption frequency and eruption volume, when the central volcano is compared with other parts of the volcanic system, is also partly due to the trap-like nature of the magma chamber. The chamber is normally much smaller than its source mantle reservoir, so that a single magma flow (through a dike) from the reservoir (lasting perhaps many years) may trigger tens of magma flows (through sheets) from the chamber, many of which would reach the surface in the central volcano. ¿ 1998 American Geophysical Union