Locking system for furniture drawers, including a rivet attached to the drawer which operates a locking device, all these locking devices are correlated through a base-plate fitted to the piece of furniture. The drawers have a height (H) such that this is a multiple of a predetermined dimension (d1). Each locking device includes a rocker, for actuation by the rivet, incorporated in a one-piece element bearing a surface cam for the rivet and a T-shaped back projection for sliding thereof in the base-plate. The height (m) of the one-piece element is such that the predetermined quantity (d1) is a multiple of said height (m); in such a way that the one-piece elements of the system interlock. The rivet is positioned at a distance (Z) from the side that is a multiple of the height (m) of the one-piece element.