A continuous casting machine has a mold of a rectangular cross-section having short sides formed by parallel runs of a pair of metallic belts and short sides constituted by parallel runs of a pair of endless loops each comprising a plurality of dam blocks. The parallel runs of each endless loop are guided by inner and outer guide rails sandwiched between the edges of the parallel runs of the metallic belts and moved in the same direction as the movements of the metallic belts and substantially in synchronism therewith. So as to vary the widthwise dimension of a slab to be cast by the mold, the inner and outer guide rails are independently movable. The endless loop comprises first and second groups of dam blocks which groups are respectively shifted widthwise of the slab by one of the guide rails and by the other guide rail, whereby the width of the slab can be varied perpendicularly to the length of the slab being cast.