We study a seismic swarm that occurred in 1989--1990 at the Alban Hills volcano and interpret the seismicity pattern in terms of Coulomb stress changes caused by magma intrusion in a local volcanic source and the extensional tectonic stress field. We first image the three-dimensional (3-D) structure of the volcano through a tomographic inversion of P waves and S-P arrival times recorded by a temporary local network. A high Vp and Vp/Vs body exists beneath the area of most recent volcanic activity, which we interpret as a solidified magma body delimiting the position of the volcanic source. We have relocated 661 events (M ≤ 4.0) using this 3-D velocity model and we have computed 64 fault plane solutions. Elevation changes, measured between 1951 and 1994 along a 33-km-long line crossing the western part of the volcano, reveal an uplift of 0.3 m. We model these data to constrain the position and geometry of the volcanic source. We compute the vertical deformation in a homogeneous half-space, testing different volcanic sources (spherical magma chamber, sill and dike). We model the Coulomb stress changes caused by the local volcanic source and the regional tectonic stress field. The inflation of magma generates an increase of Coulomb stress larger than 0.5 MPa in the area where the seismicity is located. More than 85% of fault plane solutions are consistent with the stress perturbations induced by the volcanic source. We conclude that microearthquakes at the Alban Hills are promoted by elastic stress changes caused by volcanic unrest episodes.