Large composite structures, such as composite wind turbine blades, may exhibit multiple failure modes that challenge the modeling strategies and methodologies designers adopt in finite element (FE) analysis. This study develops a comprehensive and general FE modeling method to simulate interactive failure process of composite box beams used in wind turbine blades. The composite box beams are the primary loading-carrying members and could show different failure modes due to competing failure mechanisms. A continuumdamage mechanics based progressive failure analysis approach is developed in three-dimensional stress/strain domain to simulate failure behavior of the box beams. Structural nonlinearities associated with geometry, materials and contact are included. The material failures considered in this study are composite failure with three material failure modes, foam core crushing and adhesive failure. The in-plane shear stress versus strain relation of unidirectional composites is included in the material damage model. Comprehensive comparisons are made between numerical simulations and experimental observations with respect to strain response, ultimate loads, failure modes and failure progress. The modeling approach is found to be capable of predicting both strength and failure of box beams with reasonable accuracy and it exhibits great potential to predict failure response of composite wind turbine blades.