An apparatus for conveying thick matter is provided including a delivery line, a thick matter pump connected to the delivery line for conveying thick matter from the pump through the delivery line in an output direction, and a restraining member positioned in the delivery line. The restraining member includes a first group of finger lamellae that are radially arranged and have openings therebetween. Each of the finger lamellae of the first group includes an end secured on the inner surface of the delivery line and an unattached end extending diagonally in the output direction and toward the inside of the delivery line. The finger lamella thereby define a pass-through opening therein for enabling flow of thick matter through the restraining member such that the pass-through opening increases in size when thick matter flows in the output direction and decreases in size when there is no flow of thick matter or when thick matter moves in a direction opposite to the output direction. The restraining member also includes a second group of finger lamellae which have openings therebetween and are arranged relative to the finger lamellae of the first group such that the finger lamellae of the second group at least partially cover the openings between the finger lamellae of the first group.