At present, the design and optimization of profile parameters of hypocycloid gear pump mostly use the two-dimensional geometic theory. Its geometric properties in the flow field are not considered. Therefore, the flow around model was established by using COMSOL software platform. After verification with previous experimental data，the model was applied to the two-dimensional numerical simulation of the flow characteristics of the hypocycloid cylinder. The distribution of eddy around the tooth profile and the variation law of pressure coefficient, lift coefficient and drag coefficient were analyzed.The influence of tooth profile parameters on the flow stability was further analyzed. The results show that as the boundary layer separation is gradually delayed with the increase of tooth width,the vortex shedding is delayed.With the increase of generating coefficient and arc diameter coefficient，the tooth top width is decreased, resulting in the increase of energy consumed to resist the inverse pressure gradient and the decrease of drag coefficient.Because of the fluctuation of vortex shedding, the lift coefficient changes periodically. When the generating coefficient is 1.3 and the arc radius coefficient is 0.55, the tooth top and the groove between the teeth play a synthetical role in delaying the shedding of vortexes,which can reduce the wake vortex energy,and makes the Karman vortex shedding frequency and shear layer instability frequency the lowest and the flow stability of flow around the best.The optimal value of tooth profile parameters obtained provides a basis for the design and optimization of hypocycloid tooth profile, and the analysis method can also be used as a reference for the design of products of the same type.