Unit cell modeling of woven fabric composites at meso-level has been advantageous in finding equivalent mechanical properties of different weave architectures without performing physical experiments on each new fabric. The obtained properties, in turn, can be used in the macro-level modeling and simulation of large composite structures. Models used for this purpose, however, often consider a perfect description of unit cells, while in practice fabrics are not always fabricated under ideal conditions and flaws like fiber misalignment, material and/or geometrical defects are present. A benchmark work covering effects of this kind on the mesoscopic behavior of woven fabrics is underway. The aim of this paper is to present a statistical way to approach the problem by studying the main effects of such uncertainty/noise factors along with their levels of significance. Namely, a one-factor-at-a-time screening method is selected to identify the effect of (1) fiber misalignment, (2) fiber modulus variation, (3) geometrical flaws in yarn section, (4) unpredictable friction between weft and warp yarns. Computer experiments are done using FE modeling of a plain weave unit cell under the uniaxial, equibiaxial, and trellising (shear) modes. A parameter sensitivity analysis is conducted to identify the most significant factors and the extent to which each can independently contribute to the variation of load-displacement curves (i.e., testing data non-repeatabilities).