Abstract: Thanks to the need of the technical development the problem of separation in unsteady flow is attracting more and more attention. In fact, in the 50s of this century, the investigation of More, Root and Sears led to a model of unsteady separation, known as the MRS model.Up to now,there are a lot of criteria of the unsteady separation point,such as, null vorticity criterion, the criterion derived by Change.In this paper,it is proved that an unsteady separation point must be a saddle point and the criterion for the unsteady separation point is given based on the equation of instantaneous streamline and singular point theory.The method to locate a separation point in flow field is discussed.

Key words: unsteady separation, saddle points, singularity criteria