Three-axis orthogonal woven fabric composites composed of carbon fibres and epoxy resin have been fabricated. Examined from micrographs, the fabric weaving yarns were found to be very slender with aspect ratios ranging from 11-13.6. Based upon the observed geometry, the composite has been modelled by a unit cell comprising wavy yarns. Both elliptical and lenticular cross-sections were adopted to simulate the slender weaving yarns. Taking into account one-dimensional stress concentration and yam undulation, an iso-phase approach has been developed to analyse the composite elastic moduli. A higher weaving yarn aspect ratio was found to result in a lower modulus. Modulus reduction due to yarn undulation was more significant in weaving directions. Material characterization has been conducted based upon monotonic tensile and three-point flexural tests, and detailed damage mechanisms for both loadings have been examined. The onset of damage under tensile loading was found to be z-axis yam debonding, followed by debonding and splitting in y-axis yarns. When subjected to flexural loading, yarn debonding, transverse cracking, and interyarn matrix cracking were the dominant damage mechanisms which appeared on specimen tensile sides. Stress transfer among yarns and how it relates to the composite damage have been discussed in detail.