An applicator for applying a composition to the eyelashes or the eyebrows, the applicator including an applicator member, having a core that extends along a longitudinal axis; and at least three rows of applicator elements that are molded with at least one portion of the core, the rows extending longitudinally along the core, and being arranged around the longitudinal axis of the core, the applicator elements being of cross-section that is flat, having a major axis that is oriented substantially perpendicularly to the longitudinal axis (X) of the core, at least two applicator elements having bases that are offset angularly around the longitudinal axis (X) of the core and being superposed, at least in part, when the core is observed along its longitudinal axis (X).