This paper shows the evaluation method of damage and failure of concrete for composite member such as steel-concrete composite slabs and foundation of wind turbine. The second strain invariant of deviatoric strain tensor and consumed strain energy averaged over certain region calculated from local strain were applied for the damage assessment. Owing to their complexity shapes of composite structures, FE-modeling was often required very small mesh division locally. Then, it is important that to reduce influence caused by mesh definition on assessment of output and ultimate limit state. As a result, those nonlocal damage index can assess the failure process for several types of composite structure where the damage of concrete is dominated. It was revealed that these index could evaluate the safety of composite structures by nonlinear FE analyses.