This paper investigates the problem of obstacle avoidance and path planning for robotic fish. The swimming of the robot fish to avoid some obstacles is viewed as potential flow around the obstacles. Then the streamlines from the robot position to the target are chosen as the desired paths for the mobile robot to move to the destination. Since there are mature algorithms with high computational efficiency to establish flow field and figure out the streamlines based on fluid mechanics theory, our approach is practical for application. We conduct two example experiments to verify the effectiveness of the approach.