Numerical analysis has been performed for three-dimensional and time-depending vortex breakdown in an open and confined cylindrical container flow generated by a rotating disk. Vortex breakdown in swirling flows has been the sudject of much attention since it was first recognized in the tip of delta winged aircraft. Under certain conditions vortex flows undergo sudden structural changes near their rotation axis, called vortex breakdown, which are characterized by the existence of free stagnation point upstream of a region with reversed axial flow. Recently, experimental results suggest that the asymmetry of the vortex breakdown is found to be related to the existence of asymmetric flow separation on the container wall. Adding to this, it is important to reproduce such asymmetry vortex breakdown by numerical method because there is no report to predict an asymmetric vortex breakdown numerically. In the numerical calculation, boundary fitted coordinate system has been used for this flow in order to make the cause of asymmetry vortex clear. Calculated results of angular moment and flow vectors in circular cross section are compared with the experimental data in order to examine the validity of the presented numerical method. As a result of this analysis, it has been found out that the present method can reproduce vortex breakdown reasonably for an open and confined cylindrical container. Although the present method could not predict the separated flow near the wall which has been reported experimentally as the cause of asymmetry vortex generation, we have showed numerically that asymmetry vortex is also able to be produced by shifting rotating axis from center within the gap between rotating disk and cylindrical wall of experimental apparatus.