Due to the long-range modeling ability and linear complexity property, Mamba has attracted considerable attention in point cloud analysis. Despite some interesting progress, related work still suffers from imperfect point cloud serialization, insufficient high-level geometric perception, and overfitting of the selective state space model (S6) at the core of Mamba. To this end, we resort to an SSM-based point cloud network termed CloudMamba to address the above challenges. Specifically, we propose sequence expanding and sequence merging, where the former serializes points along each axis separately and the latter serves to fuse the corresponding higher-order features causally inferred from different sequences, enabling unordered point sets to adapt more stably to the causal nature of Mamba without parameters. Meanwhile, we design chainedMamba that chains the forward and backward processes in the parallel bidirectional Mamba, capturing high-level geometric information during scanning. In addition, we propose a grouped selective state space model (GS6) via parameter sharing on S6, alleviating the overfitting problem caused by the computational mode in S6. Experiments on various point cloud tasks validate CloudMamba's ability to achieve state-of-the-art results with significantly less complexity.