This paper focuses on understanding the progressive failure behavior of woven composites. Five weaves, i.e. plain, 4-, 5-, 8-harness satin and twill, are considered. Rather than developing a new progressive failure analysis approach, the focus is placed on comparing the damage behaviors of the various weaves predicted by the selected failure criterion and property degradation model. The loading conditions include uniaxial tension and compression. The discussions focus on (1) the effect of the woven architecture on the predicted progressive failure behaviors (2) the similarities and difference in the damage initiation and evolution mechanisms between the plain and satin weaves and (3) the sensitivity of the predicted progressive failure behavior to assumptions about geometric nonlinearity and the property degradation model. The results have shown that the weave architecture (i.e. weave pattern) has significant effects on the predicted progressive failure behaviors even if the composites have the same overall fiber volume fraction, tow waviness and tow cross-section. Comparisons of the damage initiation and evolution mechanisms in the plain and 4-harness satin weaves indicate significant similarities in the damage behaviors in the comparable regions for the two weaves. The results also show that the predicted response of low waviness composite, which is more commonly seen in most structural applications, is quite insensitive to the assumed property degradation model. This imposes difficulties in validating a model by comparison with test results for low waviness composites.