A spin stabilized projectiles (1) having a rotating band (3) arranged on the shell body (2), with such rotating band being provided with grooves (35, 36, 37) to receive rotating band material sheared off toward the rear during passage of the projectile (1) through a gun barrel (4) so that the transfer of spin is effected with the aid of annular rotating band zones (31, 32, 33, 34) which form spin transfer ring. The diameter (38) of at least one spin transfer ring (31, 34), preferably the rearmost ring, is larger than the diameter (45) of the rifling grooves (42) in the gun barrel (4). Due to the high radial pressure on the shell body in the region of the rotating band, great radial deformations may occur, particularly in thin-walled shell bodies. The consequences are untightness of the rotating band and too much stress on the projectile. To overcome these drawbacks of prior art rotating bands, the diameter (39) of at least one of the remaining spin transfer rings (32, 33) is smaller than the diameter of the rifling grooves (45) but larger than the caliber (44) of the gun barrel (4).