A casting machine comprises a pair of travelling block mold assemblies (22) each having a plurality of block mold members (23) endlessly connected to one another to define a cavity (27), and a mechanism for driving the block mold members (23) such that the block mold members of one travelling block mold assembly (22) move in synchronism with those of the other in a casting direction. Latticed grooves (25, 34, 35, 36) are form on at least an area of the inner wall of each of the block mold members (23) which combine with one another to form the cavity (27). Delays in the solidification of molten steel in the cavity (27) are intentionally caused by these grooves, with the result that the concentration of contraction stress caused by the solidification delays at those seams (3) along which the adjacent block mold members (23) are connected to each other to form the cavity (27) can thus be reduced to prevent the creation of cracks on surfaces of cast products.