In a multi-core system with shared resources, the accesses to the shared resources from several cores may experience non-deterministic arbitration delay due to resource contention. Such delay should be considered conservatively in the worst case response time (WCRT) analysis of multi-core systems. Recently, several techniques have been proposed to account for arbitration delay for shared resource contention, based on the event stream modeling of resource access. While they all assume independent tasks, in this paper, we propose a conservative modeling technique of shared resource contention supporting dependent tasks. To find a tight upper bound of arbitration delay, we derive a shared resource demand bound for each processing element, considering the task dependency. The proposed technique is not specific to a particular WCRT analysis method, and supports both preemptive and non-preemptive scheduling policy. In the experiments, the significance of considering data dependency of parallel applications and the performance of our technique are verified by synthetic examples and a real-life example.