An applicator for applying a cosmetic composition to the eyelashes or eyebrows, comprising: - a core, - at least one element attached to the core, each element comprising a central part fitted onto the core and at least one application member carried by the central part, this application member (20; 20') being hollow and comprising at least one cavity (14; 14') passing through it in one direction and having a closed contour when viewed in this direction, the hollow application member being toothed at its periphery or multilobed at its periphery, the hollow application member having a strand of material extending through a complete loop, or at least one application member carried by the central part, this application member (20; 20') being hollow and comprising at least one cavity (14; 14') passing through it in one direction and having an almost closed contour when viewed in this direction, the hollow application member having a strand of material extending through an incomplete loop closed by the central part, and/or at least two adjacent application members forming at least one almost closed cavity (69; 90; 111; 156; 166; 187; 205; 225; 250) between one another, wherein each application member is flattened in a flattening plane common to all the application members of the element. - a core, - at least one element attached to the core, each element comprising a central part fitted onto the core and at least one application member carried by the central part, this application member (20; 20') being hollow and comprising at least one cavity (14; 14') passing through it in one direction and having a closed contour when viewed in this direction, the hollow application member being toothed at its periphery or multilobed at its periphery, the hollow application member having a strand of material extending through a complete loop, or at least one application member carried by the central part, this application member (20; 20') being hollow and comprising at least one cavity (14; 14') passing through it in one direction and having an almost closed contour when viewed in this direction, the hollow application member having a strand of material extending through an incomplete loop closed by the central part, and/or at least two adjacent application members forming at least one almost closed cavity (69; 90; 111; 156; 166; 187; 205; 225; 250) between one another, at least one application member carried by the central part, this application member (20; 20') being hollow and comprising at least one cavity (14; 14') passing through it in one direction and having a closed contour when viewed in this direction, the hollow application member being toothed at its periphery or multilobed at its periphery, the hollow application member having a strand of material extending through a complete loop, or at least one application member carried by the central part, this application member (20; 20') being hollow and comprising at least one cavity (14; 14') passing through it in one direction and having an almost closed contour when viewed in this direction, the hollow application member having a strand of material extending through an incomplete loop closed by the central part, and/or at least two adjacent application members forming at least one almost closed cavity (69; 90; 111; 156; 166; 187; 205; 225; 250) between one another,