The effects of a realistic western boundary current on the alongshore propagation of sub-initial waves trapped by a sloping bottom topography are studied using a numerical model incorporating realistic bottom topography and a current field which is in thermal wind balance with the density field. This models the Gulf Stream as it flows along the continental slope off North Carolina. The mean state velocity and density fields do not vary alongshore and are continuous in the horizontal as well as the vertical. The linearized, inviscid equations of motion for small amplitude disturbances yield a single governing equation for the perturbation pressure. This equation is solved using a marching method for elliptical problems. The dispersion relations are obtained by searching for the resonance response of the system to an arbitrary uniform forcing term. Four discrete stable modes of Rossby-like waves are identified, all propagating in the upstream direction. A mode-coupling resonance is found between the first two modes. For small wavenumber, the first mode is trapped within the frontal zone on the cyclonic side of the mean current with a smaller barotropic component over the shelf. This 'frontal trapping' is due to the quasi-geostrophic potential vorticity gradient in the mean current. For larger wavenumber, the first mode becomes primarily a barotropic shelf wave. The second mode is a purely barotropic shelf wave for small wavenumbers, but becomes a frontal-trapped wave at large wavenumbers. For the higher wave modes, most of the energy is trapped near the surface in the frontal zone. (Author).