To advance our knowledge in neuroscience it is fundamental to understand the complexities of the human cerebral cortex. The cortex exhibits significant variability across individuals, presenting challenges in identifying patterns at the population level. While supervised learning methods excel at such tasks, they require a large amount of labeled samples to train. This is a serious limitation due to the costly and time-consuming annotation process requiring neuroscience experts. To address this challenge, self-supervised learning (SSL) was introduced in various other domains. By pretraining models on unlabeled data, SSL reduces the dependency on large labeled datasets, as labeled data is only used to fine-tune the models for downstream tasks. In this paper, we explore the effectiveness of self-supervised pretraining on a large number of cortical surfaces from the Human Connectome Project dataset. Leveraging a masked graph autoencoder, we develop a pretrained model suitable for various downstream tasks. The model’s performance in segmentation (node classification) and age prediction (graph regression) tasks are evaluated by using cortical surfaces from the manually labeled MindBoggle dataset. Our findings demonstrate that SSL with fine-tuning outperforms models trained from sratch across both tasks. Our research contributes to advancing the application of self-supervised learning in cortical surface analysis, with implications for neuroscience research and clinical practice. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.