Abstract: An external shell as herein a support for a cosmetic applicator element slidable between a retracted position and an extended position for use of the element. The support is connected to a first rack which extends parallel with the axis of the shell but which is offset in relation to this axis. The first rack meshes with a pinion free for rotation about a pin fixed to the external shell and extending substantially perpedicular to the axis of the shell. The pinion meshes with a second rack parallel to the first but diametrically opposed relative thereto in relation thereto the pin. The second rack is solid with a sleeve which is slidable in the shell and in which the support is slidable. The cosmetic element is, in its retracted position, entirely accommodated within the sleeve and in its position for use, projects at least partially out from the sleeve.