Laminated carbon/epoxy composite structures are increasingly used in the aerospace industries. Low weight, elastic tailoring, and high durability make the composite materials well suited for replacement of conventional metallic structures. However the difficulty to capture structural failure phenomena is a significant barrier to more extensive use of laminated composites. Predictions are challenging because matrix (resin) dominated failure mechanisms such as delaminations and matrix cracking contribute to the structural failure in addition to fiber-dominated failures. A key to rigorous failure predictions for composites is availability of measurements to quantify structural model parameters including matrix-dominated stress-strain relations and failure criteria. Novel techniques for measurement of nonlinear interlaminar constitutive properties in tape composites have been recently developed at Georgia Institute of Technology. Development of methods for accurate predictions of failure in carbon/epoxy tape laminate configurations with complex lay-ups is the main focus of this work. Failures through delamination and matrix cracking are considered. The first objective of this effort is to implement nonlinear interlaminar shear stress-strain relations for IM7/8552 carbon/epoxy tape in ABAQUS finite element models and validate structural delamination failure predictions with tests. Test data for composite configurations with wavy fibers confirm that nonlinear interlaminar shear stress-strain response enables accurate failure prediction. The problem of the presence of porosity and its influence on failure was noted. The second objective is to assess the ability to simulate initiation and propagation of matrix-ply cracking. Failure models for IM7/8552 carbon/epoxy tape open-hole tensile coupons are built and validated.