We have seen a great progress in video action recognition in recent years. There are several models based on convolutional neural network (CNN) with some recent transformer based approaches which provide state-of-the-art performance on existing benchmark datasets. However, robustness has not been studied for these models which is a critical aspect for real-world applications. In this work we perform a large-scale robustness analysis of these existing models for video action recognition. We mainly focus on robustness against distribution shifts due to real-world perturbations instead of adversarial pertur- bations. We propose four different benchmark datasets, HMDB-51P, UCF-101P, Kinetics-400P, and SSv2P and study the robustness of six different state-of-the-art action recognition models against 90 differ- ent perturbations. The study reveals some interesting findings, 1) trans- former based models are consistently more robust against most of the perturbations when compared with CNN based models, 2) Pretraining helps Transformer based models to be more robust to different pertur- bations than CNN based models, and 3) All of the studied models are robust to temporal perturbation on the Kinetics dataset, but not on SSv2; this suggests temporal information is much more important for action label prediction on SSv2 datasets than on the Kinetics dataset. We hope that this study will serve as a benchmark for future research in robust video action recognition.