General point clouds have been increasingly investigated for different tasks, and recently Transformerbased networks are proposed for point cloud analysis. However, there are barely related works for medical point clouds, which are important for disease detection and treatment. In this work, we propose an attention-based model specifically for medical point clouds, namely 3D medical point Transformer (3DMedPT), to examine the complex biological structures. By augmenting contextual information and summarizing local responses at query, our attention module can capture both local context and global content feature interactions. However, the insufficient training samples of medical data may lead to poor feature learning, so we apply position embeddings to learn accurate local geometry and Multi-Graph Reasoning (MGR) to examine global knowledge propagation over channel graphs to enrich feature representations. Experiments conducted on IntrA dataset proves the superiority of 3DMedPT, where we achieve the best classification and segmentation results. Furthermore, the promising generalization ability of our method is validated on general 3D point cloud benchmarks: ModelNet40 and ShapeNetPart. Code 1 is released.