The invention relates to a nozzle (10) for fastening a material layer to a substructure, comprising a plate (12) and a hollow shank (14), integrally formed thereon, for taking a fastening screw (24; 34), wherein a stepped bore (16) is provided in the hollow shank, wherein the stepped bore (16) comprises at least two steps (28; 38; 50) between at least three regions (18; 30; 36; 2), wherein the hollow shank (14) is formed so as to taper at least partially in a conical manner on an external surface, wherein the hollow shank (14) is provided with radially expandable elements, and wherein the expandable elements are formed as axial grooves (40) externally in that part of the hollow shank (14) that is formed in a conically tapering manner. The invention proposes that the grooves (10) are each provided at the groove base at least partially with a thin bottom (42) that is stretchable or breakable by the expansion. The present invention also relates to a fastening element comprising a nozzle (10) according to the invention and a fastening screw (24; 34).