<p>Medical image analysis using computer-based algorithms has attracted considerable attention from the research community and achieved tremendous progress in the last decade. With recent advances in computing resources and availability of large-scale medical image datasets, many deep learning models have been developed for disease diagnosis from medical images. However, existing techniques focus on sub-tasks, e.g., disease classification and identification, individually, while there is a lack of a unified framework enabling multi-task diagnosis. Inspired by the capability of Vision Transformers in both patch-based and image-based representation learning, we propose in this paper a new method, namely Multi-task Vision Transformer (MVC) for simultaneously classifying chest X-ray images and identifying affected regions from the input data. Our method is built upon the Vision Transformer but extends its learning capability in a multi-task setting. We evaluated our proposed method and compared it with existing baselines on a benchmark dataset of COVID-19 chest X-ray images. Experimental results verified the superiority of the proposed method over the baselines on both the image classification and affected region identification tasks.</p>