Radiation-induced simultaneous grafting of acrylic acid onto high density polyethylene filament is carried out with aqueous solution of acrylic acid in the absence and presence of ethylene dichloride. Distribution of grafted poly(acrylic acid) is studied by two methods. One is optical microscopic investigation of cross sections of dyed filament, and the other is electron probe microscopy of acrylic acid graft filament after conversion to calcium acrylate. Qualitative study with WAXS is also carried out. Grafting begins from the surface or periphery and proceeds, with sharp boundary, to the core. The reaction takes place only in the amorphous part of polyethylene. The percent graft in the grafted part is homogeneous and rather high from the beginning of the reaction; it is true that additional grafting to the already grafted part takes place, but it is not so noticeable.