Campi Flegrei is a densely inhabited volcanic area within a caldera, 12--14 km in diameter, immediately west of Naples, Italy. In 1970--1972 and in 1982--1984, Campi Flegrei experienced considerable ground surface deformation producing a bulge about 3.5 m high at its peak. In the two inflation episodes the point of maximum uplift did not change, coinciding with the caldera center, about which the displacements exhibited radial symmetry. The 1982--1984 uplift was accompanied by considerable seismic activity. Gravity changes have been interpreted as reflecting the occurrence of a subvertical magnetic intrusion. Volcanological, petrological, and geophysical data point to the existence of a shallow magma chamber just beneath the center of the caldera. We assume that the observed surface displacements are the response of an essentially elastic medium to a pressure increase in the magma chamber. Static deformation is calculated by using a finite-element method, assuming axial symmetry around a vertical axis through the caldera center. The role played by various components of the model, geometry, boundary conditions, elastic properties, is analyzed. It is shown that models assuming uniform elasticity are inadequate. Therefore the major volcanotectonic features as well as the influence of temperature and pressure on the elastic properties are taken into account. The results of various more complex models are presented. It is suggested that the progressively fracture zone, whose size and shape depend also on the possible occurrence of magnetic intrusions, may explain the observed surface displacements and the other data collected at Campi Flegrei. it is suggested that the 1970--1972 uplift was possibly accompanied by larger-scale changes in the stress field. ¿ American Geophysical Union 1987