The disclosure describes a flame-resisting resin composition comprising:(A) 90 to 99.5% by weight of a polyarylene sulfide; and(B) 0.5 to 10% by weight of a graft copolymer composed of an olefinic copolymer (a) having 30 to 59% by weight (based on the weight of said graft copolymer) of an .alpha.-olefin repeating unit and a glycidyl ester residue repeating unit of an .alpha.,.beta.-unsaturated mono-carboxylic acid, and at least one of polymers (b) having the repeating unit represented by the following formula (I):said olefinic copolymer (a) being branched or crosslinked with at least one of the polymers (b), ##STR1## wherein R represents a hydrogen atom or a lower alkyl group having from 1 to about 6 carbon atoms, X represents a benzyl group, --COOCH.sub.3, --COOC.sub.2 H.sub.5, --COOC.sub.4 H.sub.9, --COOCH.sub.2 CH(C.sub.2 H.sub.5)C.sub.4 H.sub.9, --CN, a phenyl group or a maleimide group.