Abstract: The growth rate, phase speed and the spatial structure of the growing planetary and synoptic waves in winter and summer zonal mean flows have been investigated by the eigenvalue-eigenfunction technique based on a hemispheric and a global model including the troposphere-stratosphere-mesosphere (0-80km). The results show that the winter basic flows are able to generate three types of growing waves:the quasistationary planetary Green modes (wavenumber m=1-2),the deep Charney modes (m=3-4) and the tropospheric propagating Charney modes (m=5-9).In the summer basic flow, 2 types of growing waves exist:the westward propagating waves in the mesosphere (m=1-4) and the eastward propagating waves in the troposphere (m=5-7).The results compare with observation favorably, suggesting that a mechanism of dynamic instability of a deep atmosphere may be responsible for the observed transient planetary waves. By comparison between the results of the deep model and a few shallow models, it is concluded that a numerical model of planetary waves should at least extend to the stratopause. The traditional tropospheric models woule seriously distort structures and phase speeds of the planetary waves.