The present invention relates to an anhydrous solid cosmetic composition comprising: •a) at least one vinyl polymer comprising at least one carbosiloxane dendrimer-based unit; •b) at least two hydrocarbon-based volatile oils, •c) at least one saturated or unsaturated, preferably linear, solid fatty alcohol whose melting point is greater than or equal to 40° C., comprising from 16 to 60 carbon atoms. The invention also relates to a process for making up and/or caring for the lips, in which the abovementioned composition is applied to the lips.