Applicator (1) for a cosmetic product, typically a mascara, comprising an application means (4) having an axial core (40) which is unitary with axial rod (3) at its lower part (31) and a stack (41) of a plurality of N elements which cooperate with axial core (40) through a typically central orifice (50) allowing the axial core (40) to extend therethrough, characterized in that: the elements are elements E (5) lacking complete rotation symmetry, and the axial core (40) and the plurality of elements E (5) operate jointly with an angular orientation means for elements E (5) with respect to axial direction (10), in a transverse plane (11) which is perpendicular to the axial direction (10), in a manner that each element Ei (5) is rotatably connected with axial core (40) and has a predetermined angular orientation αi with respect to the axial core (40).