The adhesive joint is the most widely used joining technique of thermoset composite structures. Analysis of the failure of adhesive joints of composite structures has a high importance due to its significance in industrial applications such as automobile or autobus bodies. In this paper we performed experimental and numerical analysis of a glass fiber reinforced, vinyl-ester matrix composite bonded with a methacrylate adhesive. The critical energy release rate in normal loading direction obtained from standard double cantilever beam test is used as input data in finite element simulations, in which the failure process is modeled by using cohesive zone material. Results of interface elements with exponential and standard contact elements with bilinear cohesive behavior are compared. The use of interface elements is numerically robust, convergence is reached faster, but identical mesh between the parts is needed. It can be a good alternative when simulating sub-models. When using standard contact elements, the robustness needs contact stabilization, however this method does not need identical mesh and it also allows the use of shell elements, therefore it can be used on a full-structure scale with high efficiency.