A circular weaving machine in which longitudinal threads are arranged in radial groups is provided with a shed mechanism for creating shed openings in the radial groups so that a wrap thread can be passed through the openings to produce a circular weave. The shed mechanism includes operating threads connected with the longitudinal threads and arranged in corresponding groups. The operating threads of each group extend outwardly from the longitudinal threads and thence downwardly, and suspended from the depending portions of the operating threads are gripping balls. A draw bar positioned below the gripping balls carries a pick-up assembly and indexing assembly for incrementally advancing the pick-up assembly. The pick-up assembly moves in the direction in which the group of balls is arranged, and as it does it either engages or disengages the gripping balls of the group, depending on the direction of movement. When a selected number of gripping balls are engaged or disengaged, a drive assembly lowers the draw bar and this pulls the operating threads connected with the engaged gripping balls downwardly. The displaced operating threads in turn draw the longitudinal threads to which they are connected outwardly to create a shed opening in the group of longitudinal threads.