Abstract: Symmetric instabilities of non-zonal and non-parallel mean flows are discussed in this paper by using of nonhydrostatic equilibrium mode on a f-plane in which so nic wave is filtered under anelastic assumption. The new condition of symmetric instability of non-zonal mean flows has been found. In consideration of the shear of mean flows across the band distur bance, the instability condition of non-rotation stratified fluidis Ri 2 (β-α). The weak shear of mean flows across the band distur bance can't change the growthrate of symmetric instability in rotation stratified fluid under O(∈) appr oximation. The distur bance must propagate along down shear. The shor ter the waveleng this, the bigger the phase velocity is.