A method of weaving including warp and weft being supplied in the form of tapes, and not yarns. The method preferably carried out in vertical format and includes feeding positively flat tensionless warp for shedding and taking-up; selecting, feeding positively and inserting weft tapes of different widths and thickness by gripping in its fore end in flat condition; depositing inserted weft at fabric-fell in a flat condition without beating-up; and taking-up the woven material that includes either the same or different widths of flat wefts. The warps and wefts, preferably of partially stabilized type of fibrous tapes, can be overfed in a tensionless, positive and controlled manner when required to make the fibres of constituent fibrous tapes occur non-linearly in the form of wave/texture during weaving. Extra warps and wefts can be also fed in tandem whereby the warps and wefts become composed of two or more unconnected, mutually slipping, flat tapes in a stacked arrangement. These doubled warps and wefts function effectively as a unit warp and weft during weaving and in the fabric. The method also allows for the production of other materials such as those with slant weft tapes in relation to warp, having a shape within the body of the fabric and warp and weft tapes of shaped edges. A variety of fibrous and non-fibrous materials are equally well processed.