A face milling tool includes a tool body having an axial front end surface with several seats. Each seat has support surfaces for rotationally locking and supporting a tangential cutting insert in the seat. One of the support surfaces is a flat axial support surface for supporting the tangential cutting insert in an axial direction defined by the central rotation axis. The flat axial support surface extends perpendicular to the central rotation axis and is situated axially foremost in the seat. A side wall of each seat is formed out of round side support surfaces. Each tangential cutting insert includes an axial back side with a flat axial contact surface abutting the flat axial support surface and a projecting member extending axially from the flat axial contact surface and having a circumferential side surface forming out of round side contact surfaces abutting the out of round side support surfaces.