Abstract: The effects of zonal flow on the stability of linear and nonlinear orographic Rossby waves and their solutions by adopting the phase plane method under the semi-geostrophic approximation are discussed in this paper. It is shown that the criterion of nonlinear stability of the waves is the same as that of linear stability, and the effects of zonal flow and its shear on the wave stability are obvious; under the nonlinear approximation solitary wave troughs and solitary wave ridges are formed.