A micromechanical analysis of the representative volume element (RVE) of a plain weave textile composite has been performed using the finite element method. Two alternate methods for predicting failure envelopes are presented: a parametric ellipse-fitting scheme which accurately predicts trends in failure envelopes for a given failure space, as well as the formulation of a robust 27-term quadratic failure criterion to predict failure under any general plate loading conditions. A previous study by the authors extended a method, known as the Direct Micromechanics Method (DMM), to develop failure envelopes for a plain-weave textile composite under plane stress in terms of applied macroscopic stresses. The importance of consideration of stress gradient effects over the relatively large RVE dimensions of a textile microgeometry was illustrated, and it is assumed that the stress state is not uniform across the RVE. This is unlike most stiffness and strength models, which start with the premise that an RVE is subjected to a uniform stress or strain. The stress state is defined in terms of the well-known laminate theory load matrices [N], [M], i.e.force and moment resultants. Assuming that micro level failure criteria for the yarn and matrix are known, failure envelopes for a plain-weave textile composite have been constructed using the microstresses from finite element analysis of the RVE. The parametric ellipse-fitting method for predicting failure envelopes was found to agree with DMM results to within a few percent. The quadratic failure criterion was found to agree with DMM results within an average deviation of 9.3%, but the method is more robust in terms of its ability to accommodate general 6D plate loading conditions.