The present invention concerns a processing element for processing a material, like for example a sonotrode or an anvil, comprising a carrier surface which is substantially in the form of a cylinder or in the form of a segment of a cylinder and which is intended to come into contact with the material during processing, wherein the processing element is intended to be rotated about its longitudinal axis during processing so that the carrier surface rolls on the material to be processed, wherein arranged on the carrier surface is at least one structure element which projects beyond the carrier surface in the radial direction, wherein the structure element has a top side which is provided to come into contact with the material to be processed. To provide a processing element which reduces the abrupt deflection of the sonotrode when the material comes into engagement with and/or comes out of engagement with the carrier surface it is proposed according to the invention that the top side is at least portion-wise convexly curved in the peripheral direction with a radius of curvature which is less than the greatest spacing of the top side from the cylinder axis or comprises at least two surface portions which include an angle