Stroke classification for online handwriting aims at providing each stroke with a semantic label so as to fulfill handwriting segmentation. This task has attracted considerable attention due to its significance in online handwriting analysis. Existing methods are designed for the static situation, where stroke classification is conducted on the completion of handwriting. With the popularity of pad devices and electronic whiteboards, streaming stroke classification becomes increasingly important for instant handwriting processing and feedback. However, streaming classification is much more challenging due to the lack of contextual information and is underexplored in the past. In this paper, we propose Multiple Stroke State Transformer (MSST), a novel framework to enable simultaneous real-time classification and modifiability of previous predictions. Particularly, we set multiple states with duration for each stroke and then divide all states into chunks to perform message passing by Transformer. Experiments on handwritten documents and diagrams demonstrate the superiority of our method.