A continuous casting mold for casting strands, preferably of steel, includes mold plates and water boxes, and a connecting plate for connecting each mold plate to one of the water boxes. A water cooling system is formed by water conduits between the mold plates and the water boxes, wherein the water conduits are arranged in a side of the water box facing the mold plate and not in the mold plate. The water box and the connecting plate of the water box are joined together by connecting screws and nuts, wherein the connecting screws are arranged in the mold plate and the nuts are arranged on the water box. The connecting screws have internal cooling ducts and the internal cooling ducts are connected to the water conduits.