To provide the subject apparatus designed to improve the traveling stability of rapier bands while trying to reduce the vibration of the loom.

This support apparatus has such a scheme that a number of support pieces 19, 20, 21 is aligned along the longitudinal direction of a sleight 18 in front of the sleigh 18 supporting a read 17; the support piece 19 which allows the relative movement of rapier bands 15, 16 from the side of a cloth fell W1 toward the side of the reed 17 is set up within the range near the end of the width of the reed 17; the support piece 20 which determines the traveling paths for rapier bands 11, 12 as well as prevents the rapier bands 11, 12 from floating up is set up within the range excepting the proximity and range of the meeting position for a delivering rapier head 15 and a receiving rapier head 16; and the other support piece 21 which determines the traveling paths for the rapier bands 11, 12 is set up within the range near the above meeting position.