This study utilizes a shallow-water numerical model to investigate the influences of mountain topography on an approaching vortex on an f-plane. Systematic numerical experiments show that vortex track deflection is significantly dependent upon several parameters, namely the maximum tangential flow speed of the vortex (Vmax), the basic flow (U), the fluid depth (H), the radius of Vmax (R), the mountain height (h), and Lm which, in the presence of mean flow, is represented by Ly defined as the mountain half-width in the direction normal to the vortex movement. Accordingly, there exist several nondimensional parameters, the vortex Froude number, Vmax/√gH, the basic-flow Froude number, U/√gH, the nondimensional mountain height, h/H, and the nondimensional vortex size R/Lm. The northward track deflection for a westbound vortex is significantly reduced by increased U/√gH. However, the direction of track deflection is primarily controlled by R/Lm, with respect to the nondimensional height, h/H. Leftward (facing downstream) deflection can be expected with HLm/hR > 0.5 or more strictly Lm/R > 0.3, for typical conditions, h/H < 0.8. With the exclusion of explicit horizontal momentum diffusion, the vorticity budgets are essentially balanced by vorticity advection and vorticity stretching (associated with divergence) with the vorticity advection (stretching) being responsible for upstream rightward (leftward) deflection. A vortex tends to move in a clockwise path around a wider and lower mountain. With a sufficiently large h/H (high mountain), the track of a vortex becomes rightward (counter-clockwise) as a result of the more dominant vorticity advection. There is a transition of track deflection of a vortex from leftward to rightward for a decreasing mountain aspect ratio of Ly/Lx (where Lx is the mountain half width in the direction parallel to the vortex movement) which indicates that leftward (rightward) track deflection will be more dominant for a westbound (northbound) vortex past meridionally elongated mountains, such as the Central Mountain Range (CMR) of Taiwan.