Abstract: A seam welding apparatus enables, even when metallic sheets are arranged in a line in a short distance, the welding electrodes to come into contact only with the metallic sheet to be welded, so as to provide a reliable welding of the metallic sheets to form connected portions having high strength. The roller electrode 20, which has on its outer peripheral portion the conical electrode surface 21, is supported by the central axis inclined relative to the surface of the metallic sheet 50 to be welded, and there is provided the stationary electrode 30 in which the portion including the flat electrode surface 31 has the smaller thickness. The electrode surface 21 of the roller electrode 20 is brought into contact with the surface of one of the metallic sheets 50 to be welded, while bringing the electrode surface 31 of the stationary electrode 30 into contact with the surface of the other metallic sheet 50.