Unsteady flow separation of flow around a circular cylinder with periodic vortex shedding is investigated in the Lagrangian frame through analysing the features of streaklines, finite time Lyapunov exponents (FTLE) and hyperbolicity time. Locations of separation point with different Reynolds numbers (ranging from 120 to 400) are studied and compared using different criteria. It is verified that the separation point on the wall remains fixed rather than moving, which distinguishes apparently from the Eulerian description. The separation profile is visualized by the streaklines and can be revealed by the ridges of FTLE in the flow and the troughs of hyperbolicity time near the separation point. The rear-end separation is presented for Reynolds number of 400, and the separation point is found moving.