Recent advances in Deep Learning and Computer Vision have alleviated many of the bottlenecks, allowing algorithms to be label-free with better performance. Specifically, Transformers provide a global perspective of the image, which Convolutional Neural Networks (CNN) lack by design. Here we present Cross Architectural Self-Supervision, a novel self-supervised learning approach which leverages transformers and CNN simultaneously, while also being computationally accessible to general practitioners via easily available cloud services. Compared to existing state-of-the-art self-supervised learning approaches, we empirically show CASS trained CNNs, and Transformers gained an average of 8.5% with 100% labelled data, 7.3% with 10% labelled data, and 11.5% with 1% labelled data, across three diverse datasets. Notably, one of the employed datasets included histopathology slides of an autoimmune disease, a topic underrepresented in Medical Imaging and has minimal data. In addition, our findings reveal that CASS is twice as efficient as other state-of-the-art methods in terms of training time. The code is open source and is available on GitHub.