Abstract: In this paper, we apply the semi-geostrophic approximation (or the geostropic momentum approximation) to analyse and solve the barotropic and baroclinic atmospheric motion. It is shown that the horizontal nondivergent or quasi-geostrophic approximation can not reflect the nonlinear effect. The semigeostrophic approximation can not only filter out the inertial gravity waves as the quasi-geostrophic approximation, but also find the solution of the nonlinear equations. The Rossby waves obtained by the semi-geostrophic approximation possess the nonlinear characterization. The semigeostrophic approximation provides the ways to discuss the nonlinear problem.