Motivated by the observed mesoscale phenomena associated with the typhoons passing over the Central Mountain Range (CMR) of Taiwan Island, the underlying fluid dynamical aspects were investigated by numerical simulations of a barotropic cyclone interacting with a high mountain on a beta-plane. Using a modified shallow water model, a variety of flow features were revealed by monitoring the evolutions of the horizontal wind speed and the vertical vorticity during the vortex/mountain interaction. As the vortex approached to the southeastern side of the island by the planetary beta gyre, a pair of shedding vortices were formed on the lee side and was developed downstream of the mountain. Two strong hydraulic jumps emerged on the impinging of the main vortex to the wake vortices. After this impinging, the main vortex mixed with the shedding vortices and the whole vorticity patch was finally reorganized as a coherent vortex identity on the northwestern of the island. Applied to the flow features of a typhoon drifting past Taiwan, the simplified shallow water model captured many features of the observed phenomena such as upstream blocking, downstream sheltering, accelerated corner winds, and foehn and secondary vortex formation.