Galling, defined as a severe kind of adhesive wear encountered when friction occurs between two sliding surfaces under sufficient load, is a complex multiscale and multi-physics phenomenon still not thoroughly understood. Its initiation and propagation is impacted by different factors related to microstructure, surface defects or chemical composition. Currently, a normalized galling test, denoted ASTM G-98, can be used to determine experimentally a threshold galling stress of material couples. A three-dimensional finite element modeling, using ABAQUS, of this tribological test has been carried out in this work in order to investigate the mechanisms appearing during galling of 316L stainless steel in particular.