Theoretical analyses of observed vertical and horizontal ground surface deformations near active volcanoes, particularly on Kilauea volcano in Hawaii, have led to useful estimates of the location and shape of substrate magma reservoirs. One of the major shortcomings of the various existing elastic models is that they have very similar near-field vertical deformations and they do not explain observed differences between vertical and horizontal deformations. Finite element models appear to offer better fits between observed and computed data. Deformations were computed for idealized magma reservoirs of various shapes: spheres, horizontal lenses, vertical plugs, sills, and dikes of various inclinations. The measured surface deformations from the summit magma reservoir of Kilauea can be approximated by a group of vertical plugs whose tops come within 1 km of the surface deformation of the lower east rift zone of Kilauea appears best explained as being produced by increased magma pressure in a 45¿ south-dipping dike whose top is about 1 km below the surface.