In this study effect of barrier on the vortex is studied theoretically in terms of the understanding of the dynamical events associated with its blocking phenomena. A numerical model has been successfully developed for a stationary two-dimensional vortex flow in the presence of a barrier, using the full Navier-Stokes equations. The numerical results show the development of flow separation in the lee of the barrier and its formation of a secondary vortex behind the barrier. These results were compared favorably to the laboratory experiments and the field data on typhoons when encountering the island of Taiwan.