A sieve has a fine wire mesh retained by a ring and two annular casings detachably linked to each other by clamping elements for clamping the wire mesh. The edge of the flat wire mesh is firmly secured to a wire ring. The first annular casing ends in a rounded end flange and the second annular casing surrounds the rounded end flange with a radial annular step for clamping of the wire ring. The wire mesh may be gently mounted into, and out of, the sieve so that the wire mesh is not damaged.