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Distribution shift has been a longstanding challenge for the reliable deployment of deep learning (DL) models due to unexpected accuracy degradation. Although DL has been becoming a driving force for large-scale source code analysis in the big code era, limited progress has been made on distribution shift analysis and benchmarking for source code tasks. To fill this gap, this paper initiates to propose CodeS, a distribution shift benchmark dataset, for source code learning. Specifically, CodeS supports two programming languages (Java and Python) and five shift types (task, programmer, time-stamp, token, and concrete syntax tree). Extensive experiments based on CodeS reveal that 1) out-of-distribution detectors from other domains (e.g., computer vision) do not generalize to source code, 2) all code classification models suffer from distribution shifts, 3) representation-based shifts have a higher impact on the model than others, and 4) pre-trained bimodal models are relatively more resistant to distribution shifts.