Carotid artery vessel wall thickness measurement is an essential step in the monitoring of patients with atherosclerosis. This requires accurate segmentation of the vessel wall, i.e., the region between an artery’s lumen and outer wall, in black-blood magnetic resonance (MR) images. Commonly used convolutional neural networks (CNNs) for semantic segmentation are suboptimal for this task as their use does not guarantee a contiguous ring-shaped segmentation. Instead, in this work, we cast vessel wall segmentation as a multi-task regression problem in a polar coordinate system. For each carotid artery in each axial image slice, we aim to simultaneously find two non-intersecting nested contours that together delineate the vessel wall. CNNs applied to this problem enable an inductive bias that guarantees ring-shaped vessel walls. Moreover, we identify a problem-specific training data augmentation technique that substantially affects segmentation performance. We apply our method to segmentation of the internal and external carotid artery wall, and achieve top-ranking quantitative results in a public challenge, i.e., a median Dice similarity coefficient of 0.813 for the vessel wall and median Hausdorff distances of 0.552 mm and 0.776 mm for lumen and outer wall, respectively. Moreover, we show how the method improves over a conventional semantic segmentation approach. These results show that it is feasible to automatically obtain anatomically plausible segmentations of the carotid vessel wall with high accuracy.