An applicator for applying a cosmetic composition to the eyelashes or the eyebrows, the applicator including a molded applicator member including: a core that extends along a longitudinal axis; and teeth that extend from the core, the teeth being disposed in more than four longitudinal rows along the longitudinal axis (X) of the core; the teeth presenting free ends that define an envelope surface of the applicator member, the envelope surface presenting, at least at one point along its length, a cross-section of shape that is flat, having a greatest transverse dimension lying in the range 7 mm to 12 mm, and a thickness lying in the range 3.5 mm to 7 mm.