Encrypted traffic classification has become increasingly important in network security. To address the difficulty of existing architectures in collaboratively modeling spatio-temporal features, we propose BiST-Mamba, a novel dual-branch spatio-temporal Mamba network that synchronously extracts spatio-temporal features. To the best of our knowledge, this is the first work to introduce VMamba into encrypted traffic classification. Preliminary experiments on a small-scale dataset show that our accuracy and F1 scores reach 92.74% and 83.43%, respectively. The method achieves promising classification performance, demonstrating the potential of the model for effective spatio-temporal modeling.