This chapter discusses the three approaches to hole stress analysis: in-plane analysis at the hole boundary; estimation of the interlaminar stresses; and a simple, handheld-calculator method of the hole stress state. Damage stress analysis of composite structures is based on the stress state around the damaged area. The stress state analysis will include the influential aspects, such as stress concentration development, environmental degradation of mechanical properties, damage location, damage orientation and damage complexity. Delaminations are termed interlaminar matrix cracks and normally grow from intralaminar matrix cracks when the cracks terminate at a ply boundary. Structural instability under compressive loading is of the greatest concern for the loss of structural performance of a composite laminated structure from the presence of delaminations. The in-plane stress analysis of holes requires a knowledge of the in-plane laminate stiffness matrix, hole geometry and applied far-field stress state.