A cross-jet nozzle includes a rotor body, in which several channels are recessed or formed running from a nozzle tip in the direction of a stator body, in which at least two front jet nozzles are positioned in the rotor body through at least two front jet channels and oriented so that front jets of a pressurized medium emerging from the front jet channels intersect outside of the rotor body and the rotor body can be mounted to rotate around its longitudinal axis on the stator body, which can be connected to a high-pressure line connection, is introduced safely parallel into tubes by a drive unit of a lance device. The nozzle tip is provided with an outer surface so that the surface is configured convexly arched, dome-like and free of edges and the nozzle tip is formed mirror-symmetric with the longitudinal axis in profile.