An analytic model has been developed for the prediction of the three-dimensional deformation field generated by the withdrawal of magma from a sill-like storage compartment during an intrusion or eruption cycle. The model is based on the work of Berry and Sales (1961, 1962) and predicts the vertical displacement components over the areal plane. Model parameters are the depth of burial h, the intrusion half width a, the intrusion half length b, the thickness of the magmatic interior at the moment of melt withdrawal tm, and the planform aspect ratio &xgr;=a/b. The products of the model include areal deformation maps. Systematic variation in model parameters within the context of Kilauea Volcano, Hawaii, have revealed that circular and elliptical deformation patterns result from the collapse of draining rectilinear intrusions at depth. Moreover, the geometric parameters of a storage compartment may interact in complex ways to produce similar deformation patterns. The model has been applied to Kilauea Volcano for three periods of pronounced summit subsidence: (1) 1921--1927 (bracketing the streamblast eruptive phases of 1924): (2) June 1972 to December 1972, and (3) December 1972 to May 1973. Application of the model requires the simultaneous optimization of five predicted deformation features with respect to field measurements and the derivative deformation maps: (1) the vertical displacement maxima: (2) the vertical displacement gradients over the areal plane, (3) the lateral extent of the deformation field, (4) the aspect ratio of the subsidence pattern, and (5) the strike of the major axis of the deformation field. The constrained geometries and volumes of the inferred collapsed storage cavities for each period are (1) 1971--1927: depth ≂3 km, a≂1500 m, b≂4500 m, tm≂20 m, V≂540¿106 m3, (2) June 1972 to December 1972: depth ≂3.3 km, a≂600 m, b≂2000 m, tm≂1 m, V≂4.8¿106 m3, and (3) December 1972 to May 1973: depth ≂2.2 km, a≂500 m, b≂1612 m, tm≂1 m, V≂3.2¿106 m3. For 2 and 3, calculated magmatic thicknesses tm happen to be in the range (3.48--0.15 m) of measurements for sill-like bodies in deeply disected Hawaiian shield volcanoes. The fits obtained between calculated and observed deformation patterns allow quantification of the location, overall dimensions, orientation, and volume of the discrete, still molten, interior of sill-like compartments from which magma is tapped during eruption or intrusion.