An applicator for a cosmetic product, in particular mascara, comprises a twisted core and fibres which extend from the core and are retained by the core, the core extending in a main longitudinal direction, referred to as the main axis (X), the core being rectilinear along the main axis (X), and the fibres forming an envelope (E) with their free ends. The envelope (E) has four faces (F1-F4), the faces (F1-F4) each having a plane of symmetry comprising the main axis (X), each of the four faces (F1-F4) being generated by a straight line, referred to as a generating line, orthogonal to the main axis (X) and orthogonal to the plane of symmetry of the face (F1-F4), at least two consecutive faces (F1, F2) of the four faces (F1-F4) having a curved profile along the main axis (X).