A suture applying device comprises a shaft having a nose piece attached at its distal end. The shaft and the nose piece are separated by a transition region, and a needle entry lumen in the shaft permits a flexible needle to be introduced in the distal direction. The needle is able to cross the transition region and penetrate tissue held therein and enter into a return lumen in the nose piece. The return lumen is U-shaped and acts to bend the flexible needle as it is advanced. In this way, the needle passes from the nose piece through the transition region in a proximal direction, and is able to pass through tissue within the transition region generally on the opposite side of a tissue puncture from the first suture passage. The needle then exits from the device, permitting the suture attached to the needle to be drawn fully through the device. The suture may then be tied in order to close and seal the tissue penetration.