Because normally fibrous structures can only sustain tensile load, the failure criterion for linear fibrous material like yarns is very simple. One can use either the tensile breaking strain or the tensile strength. However, for planer fibrous materials such as paper and nonwoven and woven fabrics, the failure determination is not as straightforward, simply because the tensile strength of these materials is dependent on the loading format.Prediction of fabric strength under complex loading has its significance both theoretically and practically. Fabrics are not only highly anisotropic, but also dimensionally unstable, very susceptible to external loading and to its historical situation. The important fabric properties critical to structural applications include the tensile strengths, the in-plane shear strengths, and the normal compressive (in thickness direction) strength, as well as the in-plane compressive strength, better known as the buckling strength.The Tsai-Wu failure criterionis utilized by Pan and Yoonto woven fabrics, assuming it is valid for woven fabrics at least at the first quadrant where failure stresses are all tensile. The unknown coefficients in the failure criterion are determined based on the experimental results. The fabric shear strength, which is an important property of fabrics in load-carrying applications but is not very convenient to obtain experimentally, is predicted based on the measured uniaxial tensile strengths of the fabric at the principal and the off-axial directions. The influences of the various directions of the off-axial tensile test on the predictions of the fabric shear strength are also studied.