The flow around a circular cylinder oscillating transversely in a uniform flow is studied to clarify the influence of the near wake of the cylinder on the stagnation flow by flow visualization techniques. Under a constant amplitude of the oscillating velocity of the cylinder, as the frequency of the oscillating cylinder increases the maximum displacement angle of the stagnation point exceeds the maximum angle of the incidence of the main flow to the cylinder. At the frequency of the cylinder synchronized with the shedding frequency of the vortex the displacement of the stagnation point is closely related to the structure of the vortices near the cylinder. At the other frequency of the oscillating cylinder it is rather closely related to the configuration of the separated shear layers. The displacements of the stagnation point can be estimated accurately with the potential flow model with a group of vortex filaments corresponding to the real flow in the near wake of the cylinder.