We introduce a convolutional neural network model for unsupervised learning of depth and ego-motion from cylindrical panoramic video. Panoramic depth estimation is an important technology for applications such as autonomous robotic navigation, virtual reality, and 3D modeling. In contrast to previous approaches for applying convolutional neural networks to panoramic imagery, we use the cylindrical panoramic projection which allows for the use of the traditional CNN layers such as convolutional filters and max pooling without modification. Our evaluation on synthetic and real data shows that unsupervised learning of depth and ego-motion on panoramic images increases depth prediction accuracy in comparison to training on perspective images which have a narrower field-of-view.