This paper presents the results of numerical investigation concerning failure in the corner radius of a composite laminate under outofplane load. A finite element model which consists of continuous shell elements and cohesive elements is developed using ABAQUS finite element code. In the model, hashin criteria is used to determine the interlaminar damage; and the delamination between plies is simulated via cohesive elements. Failure in the corner radius of a composite laminate under outofplane load is investigated. Some conclusions are obtained based on the results: the finite element model is so useful that the delamination in the corner radius and the loading capacity of composite laminate can be well predicted.