Abstract: In this paper, the accelerating feature of solar wind flow from subsonic and sub-Alfven velocity into supersonic and super-Alfven velocity is discussed in the axis-symmetric magnetic flux tube. In addition to the critical sonic line M²=1, there are critical Alfven line M_A²=1 and line M²+M_A²=1 if the two-dimensional effects of the flow and magnetic field are included. In this case, there is thrice transitions for the solar wind flow in the magnetic flux tube, and the type of the magnetohydrodynamic equations will change from elliptic ones into hyperbolic ones, then the elliptic, and at last, into the hyperbolic ones. The consistent solutions of the magnetohydrodynamic equations for the solar wind flow need to study, because the typical sonic velocity has the magnitude of order just the same as the typical Alfven velocity and the rapid expansion of the magnetic flux tube is interested. There may exist several transitions for solar wind flow in the local flow tube.