We examine numerically the uniaxially compressed stability of triaxially woven fabric (TWF) composites employing a proposed geometrically nonlinear finite composite plate element model with volume segmentation ABD constitutive relation, taking advantage of greatly reduced degrees of freedom. From satisfactory agreement with results from literature, numerous boundary conditions are explored for various aspect ratios in the buckling analysis. High dependencies of post-buckling patterns on plate aspect ratios are observed, from which a computationally time-saving characteristic equations have been defined before the occurrence of post-buckling state for practical convenience, best described on the basis of logarithmic critical buckling load and stiffness factor. These buckling characteristics have a direct general correlation to TWF's aspect ratios and boundary rigidities. © 2016 The Author(s).