To produce can bodies, a continuous can jacket is disclosed, that is sealed by way of a first joint is produced from a flat metal material. At least one sealing element is mounted on the continuous can jacket by way of an additional joint. At least one of the additional joints is configured as a laser welding seam, which forms an annular continuous sealing seam between the continuous can jacket and the sealing element(s). Before the sealing seam is welded, complementary seam contact surfaces of the can jacket and the sealing element are configured as annular continuous edge regions that flare out of narrow towards the can axis. To weld the sealing seam, the can jacket and the sealing element(s) are pushed together until the edge regions make contact, one of the end faces of the two edge regions lying on the interior of the can body and the other lying on the exterior of the body. This enables the air-free welding of the seam contact surfaces, thus guaranteeing an impermeable welding seam even with the use of extremely thin metal sheets. The material overlap in the vicinity of the sealing seam is minimal.