Abstract: Continuously variable cutting apparatus for elongated sheet members that are continuously supplied in a longitudinal moving direction and at desired intervals of widths; comprising several first projection nozzles connected to a high-pressure liquid source, the first nozzles being disposed to form at least two rows that extend transversely relative to the moving direction; and at least one second injection nozzle connected to a high-pressure liquid supply source, arranged to be driven to move transversely relative to the moving direction, said second nozzle being provided at a downstream position of the sheet members, below the first nozzles.