Self-supervised learning (SSL) is an efficient pre-training method for medical image analysis. However, current research is mostly confined to certain modalities, consuming considerable time and resources without achieving universality across different modalities. A straightforward solution is combining all modality data for joint SSL, which poses practical challenges. Firstly, our experiments reveal conflicts in representation learning as the number of modalities increases. Secondly, multi-modal data collected in advance cannot cover all real-world scenarios. In this paper, we reconsider versatile SSL from the perspective of continual learning and propose MedCoSS, a continuous SSL approach for multi-modal medical data. Different from joint representation learning, MedCoSS assigns varying data modalities to separate training stages, creating a multi-stage pre-training process. We propose a rehearsal-based continual learning approach to manage modal conflicts and prevent catastrophic forgetting. Specifically, we use the k-means sampling to retain and rehearse previous modality data during new modality learning. Moreover, we apply feature distillation and intra-modal mixup on buffer data for knowledge retention, bypassing pretext tasks. We conduct experiments on a large-scale multi-modal unlabeled dataset, including clinical reports, X-rays, CT, MRI, and pathological images. Experimental results demonstrate MedCoSS’s exceptional generalization ability across 9 downstream datasets and its significant scalability in integrating new modality data. The code and pre-trained model are available at https://github.com/yeerwen/MedCoSS.