For many applications in image analysis, learning models that are invariant to translations and rotations is paramount. This is the case, for example, in medical imaging where the objects of interest can appear at arbitrary positions, with arbitrary orientations. As of today, Convolutional Neural Networks (CNN) are one of the most powerful tools for image analysis. They achieve, thanks to convolutions, an invariance with respect to translations. In this work, we present a new type of convolutional layer that takes advantage of Bessel functions, well known in physics, to build Bessel-CNNs (B-CNNs) that are invariant to all the continuous set of possible rotation angles by design.