S-S relationships and progressive damage of a glass fabric composite were studied at multi-axial stress state when normal (σ1 andσ2) and shear (τ12) combined stresses were simultaneously applied to thin-walled tubular specimens parallel to the material axes. The experimental results revealed that the S-S relationships in both normal directions were represented by two straight lines intersecting each other at their knee points while the S-S curve in shear is curvilinear and convex downward. Initial yielding surface could be represented by quadratic whose bottom is square and the height is given by the shear yielding stress. The Hill's yield criterion is not applicable to predict the non-linear S-S relationships after yielding. The material failure envelope at multi-axial stress state was given by a combination between the maximum stress theory and Tsai-Wu failure criterion.