Abstract: By using the primitive equations of motion in spherical coordinates, free oscillations of the atmosphere are discussed. These equations are linearized in relalion to the atmospheric basic state. The easterly, as well as westerly mean zonal wind profile, and the associated geopotential profile are included in the basic state. Numerical method is applied to obtain the characteristic wave solutions. The eigensolutions by 2-order difference scheme are compared with those obtained by utilizing 4-order difference scheme. The eigensolutions for basic state at rest are also compared with those obtained under the assumption of a basic state with zonal wind profile of jet and non-jet type. Some discussion about how to apply the results to data assimilation is also made.