Molded one-way snap fastener comprises a stud head having a base flange and radial fins extending up from its center to a circular top. The top has downward barbs spaced between the fins. The socket has a base flange and a sleeve having a tapered mouth with a throat and an annular downwardly and outwardly inclined bearing surface above the throat and a cylindrical opening thereabove. The dimensions of the parts are such that once the stud head is inserted into the socket and the barbs pass the throat, they spring out and contact the side walls of the cylindrical opening, immobilizing the stud head in the socket. After that, attempts to unsnap the socket result in the butting of the ends of the barbs into the bearing surface, which because of its downward and outward slope, spreads the barbs causing them more resolutely to defy unsnapping. The fastener must be destroyed to give up its snapped state.