The present invention relates to an aqueous cosmetic composition in flexible solid form, comprising:at least 12 wt.-% of one or more anionic surfactants, andone or more polymer conditioning agents,said composition comprising at least one anionic surfactant selected from among acyl isethionates.The composition is preferably suitable for use as a composition for cleaning or washing keratin materials, particularly hair.The invention also relates to a cosmetic treatment method intended in particular for the care, cleaning and/or conditioning of keratin materials using said composition.