The present invention relates to a cosmetic composition for caring for and/or making up keratin fibres, in stick form, which can be applied dry, (i), in the form of an emulsion comprising a fatty phase dispersed in an aqueous phase, the said fatty phase comprising carnauba wax and/or synthetic beeswax, in a content of at least 2% by weight relative to the total weight of the said composition, and (ii) having a shear hardness of between 375 g/m and 5000 g/m, the said shear hardness being measured at 20° C. on a cylindrical stick using a rigid tungsten wire 250 μm in diameter, by advancing the wire relative to the stick at a rate of 100 mm/minute. The invention also relates to the process for coating keratin fibres comprising at least one step of applying a composition in accordance with the invention.