Abstract: A liquid-cooled casting die for the continuous casting of thin steel slabs has a molding casting die body made of a material of high heat conductivity, such as copper or a copper alloy. Preferably the casting die body is made, in each case, of two broad-side walls, situated facing each other, and narrow-side walls limiting the width of the billet, the broadside walls forming a funnel-shaped pouring-in area. In order avoid the formation of cracks in the thermally and mechanically more stressed areas of the copper plate, cooling zones are arranged particularly in the bath surface area having higher surface-related heat flow.