A fabric with a rib structure, in particular a false boucle carpet, with cut pile (13) and/or pile loops (12) is formed by a method for weaving such a fabric. On a weaving machine, such as a rod weaving machine, a backing fabric is woven by bringing weft yarns (1), (2), (3) between warp yarns (4-9) in successive weft insertion cycles, alternately weaving in warp yarns (7), (8) in the backing fabric and rib-formingly passing them around over at least one weft yarn (3). In a number of weft insertion cycles a loop-forming element (10), such as for example a wire or a wire with a blade, is provided above the backing fabric and at least one pile warp yarn (7), (8) is loop-formingly passed around over this loop-forming element (10). This method enables weaving of a fabric with a very varied appearance, because apart from the false boucle effect, areas with pile loops (12) and/or areas with cut pile (13) can also be obtained.