For the shot peening of a pipe inner wall of a curved workpiece (200) having a workpiece bore (201), use is made of a flexible blasting abrasive feed hose (10) having blasting nozzle head (20). The latter is guided through a supporting element (30) which is applied to one workpiece end (203). The blasting abrasive feed hose (10) together with the blasting nozzle head (20) is introduced into the workpiece bore (201) and advanced along a blasting treatment section therein, and subsequently retracted into the supporting element (30) again. The blasting abrasive is emitted during the advancing movement and/or during the retraction movement. A blasting nozzle unit (100) suitable for carrying out the method comprises a flexible blasting abrasive feed hose (10) and a blasting nozzle head (20) connected to the blasting abrasive feed hose (10). The blasting nozzle head (20) has a plurality of nozzle openings (21) distributed around the circumference. The outer circumference of the blasting nozzle head (21) is smaller than the inside diameter of the workpiece bore (201) in a workpiece (200) to be processed. The blasting abrasive feed hose (10) is guided in a supporting element (30) and this element (30) is guided in a displaceable manner in a stationary bearing element (40).