Stress-strain responses in tension, compression, and shear of a five-harness satin weave carbon/epoxy composite and a four-harness satin-weave glass/epoxy composite have been examined. Damage progression under tension was examined by optical microscopic inspection of the polished edges of the specimens. Models for elastic property and failure predictions of woven-fabric composites were examined and correlated with the experimental data. Damage inspection of the carbon/epoxy composite under tension revealed that the initial failure was cracking of pure matrix regions followed by transverse bundle cracking. Fill/weft debonding and longitudinal splits of the fill bundles occurred close to ultimate failure of the composite. The glass/epoxy composite displayed damage in the form of fill/weft debonding and longitudinal splits, but no transverse yarn cracking. The damage observed in both composites was confined to the region where ultimate failure occurred. Elastic properties of the composites were overall in good agreement with micromechanical predictions based on uniform strain, but failure stress predictions were less accurate.