The purpose of this study is to observe the unstable flow seen on the cone circumference in the measurement of shear property for the surfactant solutions with a cone-plate type of Rheometer. The surfactant solutions used for the experiment are six kinds of CTAB/NaSal solutions having different NaSal concentrations. In the visualization results at circumference of cone, the instability of liquid surface notably appeared in the fluids with low NaSal concentration, and it was considered that the property of shear flow at higher shear rate was closely related to the unstable flow. Furthermore, the value of critical shear rate at which flow instability appears decreases with the increment of relaxation time of surfactant solutions. Therefore, the correlation between both results suggested the existence of elasticity induced by the structural change of micelles.