The present invention relates to an applicator for applying a cosmetic product to the eyelashes and/or eyebrows, having an applicator member (8) having: —a core of thermoplastic material having a longitudinal axis, the core being twisted through more than one revolution about its longitudinal axis under the effect of the twist of the metal arms of the holder, and having an endpiece that has no spikes. —spikes of thermoplastic material extending from the core, —a holder having two metal arms twisted around the core.