A spongelike structure or a powder having fibers three-dimensionally arranged therein with high dispersibility, whose apparent density can be designed depending on the purpose or utility, as well as a process producing it. A fiber dispersion in which fibers having a number mean diameter in a predetermined range are dispersed in a dispersion medium, and this fiber dispersion is dried to remove the dispersion medium, thereby, a spongelike structure and a powder are produced.