The invention concerns an anchoring device (1) for fixing elements of a particular type on a flat surface (3), preferably tensioned, such as shrouds, riggings, cable. The device is in the form of two mutually secured plates (3, 4), one (3) generally designed to be pressed against an inner surface of a flat surface (2), being integral with a socket (5) capable of being positioned opposite a perforation of the flat surface (2), the socket (5) containing a bundle of flexible fibers (6) flared at one end to form at least one layer (6A) enclosed between the two plates (3, 4), the bundle of fibers (6) projecting outside the socket (5) to act as an anchoring point to an element of a particular type connected to the bundle (6).