The paper describes an investigation examining damage responses and failure characteristics of unidirectional graphite/epoxy composites containing a central circular hole subjected to off-axis uniaxial tension. A recently developed damage mechanics model is extended to determine the progressive damage process around the hole and the effect of such damage on the in-plane behaviors and final failure of the notched composites. The generalized stress and strain constitutive equations and the relationship between the damage variable and material properties are briefly outlined first. The anisotropic mechanical behavior of the composites is investigated by using a nonlinear finite element procedure incorporated with the damage-coupled constitutive equations. As the failure of fiber reinforced composite materials may basically be either fiber dominated or matrix dominated, separate damage criteria are proposed to capture fiber failure and matrix or fiber/matrix interaction failure in unidirectional composites. The damage model is validated by comparing the numerical prediction and experimental data obtained from a Moiré interferometry technique. Preliminary results indicate that the proposed damage model provides an effective alternative method to study progressive failure behavior in unidirectional composites.