Abstract: For supporting and cooling the reverse surfaces of belts in apparatus for continuously casting metal strip between such belts, means enclosing the reverse surface of a belt includes a multiplicity of guiding faces that are distributed closely both crosswise and lengthwise of the belt to define an intended belt path, and that have nozzle openings through which liquid coolant is projected against the belt, rapidly flowing out in a layer over the guiding face and being withdrawn at localities close to all of the guiding faces. The belt, which may be forced toward the faces to stabilize it in its desired path, thus rests on a layer of rapidly moving liquid coolant, which affords efficient heat removal and an essentially complete liquid bearing, such apparatus and procedure being also deemed applicable to cooling other surfaces.