Provided is a solid anhydrous composition that comprises particles comprising a core containing at least one beneficial agent and an envelope surrounding the core. The envelope comprises at least one hydrophobically modified polysaccharide and at least one water-soluble carbohydrate and/or water-soluble polyol. The particles simultaneously have a poured powder density ranging from 300.0 g/l to 600.0 g/l and an absolute density of greater than 1.0. The envelope also comprises at least one structuring agent. Also provided is a cosmetic process for caring for and/or for the hygiene of and/or for conditioning and/or for fragrancing and/or for making up keratin material. The process comprises applying to the keratin material the above composition. Also provided is a cosmetic process for treating body odor and optionally human perspiration, which comprises applying to a keratin material a composition defined above comprising at least one deodorant and/or antiperspirant in free form and/or in encapsulated form.