A concealed zip fastener is provided with a series of spaced element-receiving openings aligned longitudinally along a reinforced marginal edge of each of two opposed carrier tapes and defining a line of fold along which the tape is folded. These openings are adapted to hold therein a portion of an interlocking fastener element of a meandering form. A row of fastener elements is secured to the folded edge of the tape by a line of stitchings running closely along said series of openings in a manner that the tape resists lateral displacement when lateral stresses are applied in a direction to pull apart the junction of the opposed tapes.