A clamp for occluding the lumen of a tubular conduit in the human body, such as an artery, a vein, or an intestine. The clamp includes a clamp body, grip means mounted to the clamp body, and a flexible band having an axis of length and of width. The band is attached to the body at a first point along its axis of length, and is gripped by the grip means at a second point along its axis of length. A loop is formed that bounds an opening having an axis, around which axis at least 270.degree. of the peripheral boundary of the opening is formed by the flexible band. In use, the loop is formed around the tubular conduit to be occluded, and the band is drawn tightly against it by shortening the length of the band so that the cross-sectional area of the lumen is gradually closed. The band is preferably stiffly flexible so as to be shape-retaining. A worm screw can be engaged to the band to serve as means for driving the band to lessen the cross-section of the opening.