A fastening device (100), for fastening to a plate-like element, has a head (110) and a foot (120). The foot (120) has: a core (121) extending from the head (110) along an axis of rotation; and at least one group of blades (122) which are elastic at least in regions and extend outwards from the core (121). Each of the blades (122) has an oblique shoulder (123) or a shoulder with a finely stepped gradation, formed on the outer edge of the corresponding blade (122), said outer edge being arranged towards the head (110). The oblique shoulder (123) or the individual steps of the gradation of the shoulder is inclined with a slope with respect to a plane which has the axis of rotation of the core as a perpendicular. The shoulders (123) of the blades are arranged at different heights from one another along the axis of rotation.