The maximum weavability limit is predicted by extending Peirce's geometrical model for non-plain weaves for circular and racetrack cross-sections by soft computing. This information is helpful to weavers in that attempts to weave impossible constructions can be avoided, thus saving time and money. It also helps in anticipating difficulties in weaving and in taking the necessary steps in warp preparation. The relationship between the cover factors in the warp and weft directions is demonstrated for circular and racetrack cross-sections for plain, twill, basket and satin weave. Non-plain weave fabric affords further flexibility for increasing fabric mass and fabric cover. As such, they enlarge the scope of the fabric designer.