Abstract: In the case of steady, 2-dimensional separation, separation point is of a critical type. The limiting streamlines on the wall from both sides of the separation point run into the point and then depart away from the surface of the body with a certain angle. According to the definition of a critical point and the condition that the normal velocity closed to the separation point is non-zero, the separation criterion for steady, 2-dimensional flows can be deduced as follows: The friction stress at the separation point vanishes and There is a reversed flow after the separation. In the case of steady 3-dimensional separation, there is a separation line which starts at a saddle point and ends at a separated nodal point, as well as a separation sheet which consists of streamlines originating from a critical point. This critical point can be viewed as a saddle point topographically on the wall, or as an attached nodal point in the section containing the separation line and perpendicular to the wall. Based on the theory of singularities and topological rule, there may exist a half saddle point in the section cut normally to the wall and separation line. As a result, it can be argued that the argument about the limiting streamlines must rise before approaching separation line, due to Lighthill, is incorrect. This paper shows that the limiting streamlines along the wall always coincide with the corresponding friction lines. Limiting streamlines are attached to the wall until the separated nodal point or saddle point where they lift off the wall. Finally, the paper also presents the separation criterion for steady 3-dimensional flows which is different from that for 2-dimensional flows.