PURPOSE: To prevent the hand of fibers and nonwoven fabrics subjected to flame retarding processing from deteriorating.

CONSTITUTION: A base material of fibers and nonwoven fabrics is subjected to softening finish treatment before irradiation with electron rays and the graft copoymerization of vinyl phosphonate is then carried out by irradiation with the electron rays to perform flame retarding processing. The base material is initially impregnated with the softening finish agent and then dried. The dried base material is subsequently irradiated with the electron rays in an inert gas atmosphere to carry out the graft copolymerization of the vinyl phosphonate with the base material to which the softening finish agent is applied. The impregnation of the softening finish agent and the vinyl phosphonate may simultaneously be carried out. The softening finish agent in a state thereof enclosed in the vinyl phosphonate is fixed to the base material. The base material has softness and the softening finish agent does not peel even by washing to retain the softness.