Damage and mechanical properties in textile composites are closely connected with the textile reinforcement's internal structure. This paper reports and discusses a study of the mechanical behavior and damage of a 2 x 2 twill woven carbon/ epoxy composite resulting from uniaxial tension in the warp and bias directions. A damage investigation was performed by using acoustic emission and full-field strain optical measurements, as well as X-ray and optical microscopy. As a result of the tests, the mechanical properties and strain values of the composite's damage threshold were determined. Damage initiation when loaded in the warp and bias directions occurred between 0.2% and 0.3% and 0.88% and 1.71% of the applied strain, respectively. Microscopic examination showed that damage or cracks initiated where the yarn was crimped and at interactions between the warp and filling yarns. Full-field strain measurements highlighted the relation between the strain concentrations that are linked with the damage initiation and the reinforcement structure.