Gradient vector flow (GVF) snake shows high performance at capture-range enlarging and boundary concavity convergence, however, the initial contours encounter a so-called critical point problem (CPP). The initial contour must contain the critical points inside the object and exclude those outside the object, otherwise, the final result would be far from the expected. This paper investigates the CPP of the GVF snake and points out that, serving as an external force field for snake models, gradient vector flow could be effective only under some restrictions. Also, it is proved that the theoretical foundation, the Navier-Stokes equation for viscous fluid flow, for the solution to this CPP in literatures is incorrect. Finally, an empirical solution to the CPP is presented and its performance is validated by experiments.