Analyzing brain structures in medical imaging poses challenging problems due to heterogeneity in pediatric diseases. Besides, measuring brain changes quantitatively is crucial to evaluating clinical outcomes related to anatomical factors. From an artificial intelligence perspective, establishing correspondences between nonrigid shapes often requires computing similarity-based measures that, in most cases, are unavailable. This paper proposes an unsupervised probabilistic framework for shape matching on brain structures by using variational unsupervised learning. Our approach comprehensively captures the underlying representation of surface descriptors related to brain structures. Then, we learned group-wise latent space representations of these descriptors using a variational derivation of the Gaussian process latent variable model, which matches the resulting features to establish unsupervised correspondences. The experimental results show how the model captures non-linearities in nonrigid brain structures in real-world neurodevelopmental data. These results demonstrated that the proposed model is suitable for monitoring anatomical changes in healthy and abnormal brain shapes.