Novel woven materials, producible by a new weaving method, are described that comprise single or doubled warps and wefts in the form of tapes that are preferably partially stabilized type of fibrous tape. These fibres are caused to occur in a non-linear arrangement during the weaving process. The non-linear fibres can be subsequently straightened by pulling the tape longitudinally. The doubled warps and wefts comprise disconnected tapes. Such separateness of constituent tapes of doubled warp and weft tapes enables them to be slid/slipped relative to each other by pulling longitudinally and laterally without causing any alteration in the woven structure. These novel fabrics solve the problem of uneven fibre distribution and orientation arising from crumples/wrinkles due to compression and stretches due to extension, at the inner and outer sides respectively, when tape-woven fabrics are curved into shapes. Further, by using doubled warps and wefts fabrics with relatively flat/planar sections and thicker/raised wide rib sections can be also created that resemble a bit like a profiled material in its cross-section. Other fabrics like those comprising slant/oblique weft tapes, shaped warp and weft tapes, formed shape within its body are also producible.