We integrate geologic, structural, leveling and Differential SAR Interferometry data to show that Vesuvius began to spread onto its sedimentary substratum about 3,600 years ago. Moreover, we model the detected deformation with a solution of the lubrication approximation of the Navier-Stokes equations to show that spreading may continue for about 7,200 years more. Correlation of volcanic spreading with phases of the eruptive activity suggests that Plinian eruptions, which are thought to pose the major hazard, are less likely to occur in the near future.