A twin-drum continuous casting apparatus for casting a metal sheet (4) by supplying molten metal (3) to a pouring basin formed by a pair of cooling drums (1) rotating in opposite directions, and side gates (2), to cool the molten metal (3) by contact with surfaces of the cooling drums (1), thereby forming a solidified shell. The cooling drum (1) is formed from a drum body (11) having shaft portions at opposite end portions, and a drum sleeve (10) fitted on an outer peripheral portion of the drum body (11). Also, means is provided for preventing various adverse influences due to differences in thermal expansion of constituent members of the drum body (11) during casting. Thus, the reliability of the apparatus is increased, and the quality of casting is improved.