Machine Reading Comprehension (MRC) is an important testbed for evaluating models' natural language understanding (NLU) ability. There has been rapid progress in this area, with new models achieving impressive performance on various MRC benchmarks. However, most of these benchmarks only evaluate models on in-domain test sets without considering their robustness under test-time perturbations. To fill this important gap, we construct AdvRACE (Adversarial RACE), a new model-agnostic benchmark for evaluating the robustness of MRC models under six different types of test-time perturbations, including our novel superimposed attack and distractor construction attack. We show that current state-of-the-art (SOTA) models are vulnerable to these simple black-box attacks. Our benchmark is constructed automatically based on the existing RACE benchmark, and thus the construction pipeline can be easily adopted by other tasks and datasets. We will release the data and source codes to facilitate future work. We hope that our work will encourage more research on improving the robustness of MRC and other NLU models.