Stability of rectangular triaxial weave fabric (TWF) composite plate with simply supported edges that is subjected to uniformly distributed biaxial compressive forces, Nx and Ny, is investigated for various load intensities and aspect ratios. TWF unit cell is discretized using 2D composite finite element of non-conforming types adopting Lagrange and Hermite interpolation functions for in-plane and out-of-plane degree of freedoms, respectively. In addition, homogenized and segmentation methods are used for the material descriptions of the plate. For the solution, eigenvalue analysis is employed in obtaining the critical buckling loads of the assembled global stability governing equation. In general, TWF plate’s aspect ratio plays somewhat greater role on biaxial stability than that of load intensity.