Matrix failure and delamination are the two dominant damage modes that govern the out-of-plane strength of the curved composite laminates. In this work, the out-of-plane failure behavior of curved CFRP laminates of different stacking sequences, namely, uni-directional [0]20, cross-ply [0/90]5s and multi-angle [45/0/-45/90/0]2s are studied experimentally and numerically. Digital image correlation and acoustic emission techniques are used for in situ monitoring of intra/inter-laminar damage modes under four-point bending load. A detailed fractography study is carried out to assess the damage modes and the failure mechanisms of the curved specimen. Subsequently, a finite element based progressive damage model (PDM) comprising of the 3D Hashin failure criteria and cohesive zone model is developed in Abaqus finite element software for simulating the intra/inter-laminar damages. The importance of combining matrix damage models with CZM and their synergy on the out-of-plane failure is studied and validated with experimental observations. The PDM model is then used to investigate the effect of stacking sequence, matrix tensile strength, and delamination strength on the failure of multi-angle curved laminates. This numerical study show insights to improve the out-of-plane strength of curved laminates by appropriate selection of laminate stacking sequence and matrix strength properties. © 2020 Elsevier Ltd