A method of casting molten material into a strip-shaped product having substantially intended final dimensions that first supplies molten material into the interior of a vessel having a casting nozzle connected thereto. The nozzle is formed of a refractory ceramic material and has a passage extending therethrough from an inlet opening connected directly to the interior of the vessel to an outlet opening. The nozzle is oriented relative to the vessel so that the outlet opening is positioned at a location higher than the inlet opening. Molten material passes from the vessel interior directly through the inlet opening and into the passage until an upper level of molten material in the passage is the same as an upper level of molten material in the vessel interior and below the outlet opening. Solidification of the molten material is commenced in the passage, thereby forming solidifying material. The solidifying material is moved through the passage in a direction toward the outlet opening, during which the material further solidifies. The thus further solidified material is discharged from the outlet opening by imparting to the nozzle, and thereby to the material, ultrasonic vibrations including at least one vibration component in the direction toward the outlet opening.