The present invention relates to an aqueous cosmetic composition which is in the form of a flexible solid, comprising: from 25% to 70% by weight of one or more anionic surfactants and one or more types of non-hollow solid particles, said composition comprising at least one anionic surfactant chosen from acylisethionates, preferably having an acyl group containing from 6 to 30 carbon atoms. Said composition is of preferential use as a composition for cleaning or washing keratin materials, in particular the hair.The invention also relates to a cosmetic treatment process, in particular for caring for, cleaning and/or conditioning keratin materials, using said composition.