Abstract: A mold assembly for continuous casting has a plurality of open-ended molds. The mold assembly further has a cooling member which is common to all of the molds and cooperates with each mold to define one or more cooling passages therewith. The cooling member, which is provided with one or more pairs of coolant inlet and outlet bores, is in the form of a cooling jacket or in the form of a back-up plate depending upon whether the molds are tube molds or plate molds. The mold assembly is rotatably mounted on a mold table having a casting location at which a mold is positioned during a casting operation. A coolant supply and coolant discharge conduit are arranged in the mold table adjacent the casting location. In operation, one of the molds of the assembly is positioned at the casting location with the remaining molds being in standby positions. At least one pair of the coolant inlet and outlet bores in the cooling member is aligned with the coolant supply and discharge conduits in the mold table.