Using the equatorial β-plane Boussinesq approximate equations for the tropical atmosphere,study is performed of the stability of Kelvin wave and zonal symmetric disturbances in zonal shear flow.Results show that only the meridional horizontal shear,when available in the basic flow,doesn't lead to unsteadiness of Kelvin wave but leads to somewhat differing phase velocity of the wave propagation at different latitudes.The physical variables,e.g.disturbance geopotential and disturbance windspeed ,have their y-direction distributions independent of basic flow.Only with vertical shear flow considered，the Richardson number (Ri>2) must be satisfied to produce stable Kelvin wave propagating east with respect to mean flow.The vertical shear in the basic flow does not lead to the instability of Kelvin wave but to Doppler frequency shifting of its phase velocity.Disturbance geopotential and velocity have their meridional distributions dependent on the vertical shear.For wind vertical shear>0(<0),the lower (higher) troposphere disturbance geopotential and velocity are attenuated swiftly in the meridional direction.For weather systems symmetric about a latitude circle,low-latitude internal inertial gravity wave is bound to display instability as long as wind vertical shear is big enough to meet Ri< 1.The present work presents the criterion of unsteadiness of the disturbance for smaller vertical shear of basic flow (Ri>1).Horizontal windspeed shear,if bigger than a critical value associated with vertical wavenumber m,factor β,hydrostatic stability N2 and Richardson number Ri,leads to instability of equatorial internal inertial gravity wave on the y-z plane,which thus causes zonally symmetric disturbances to emergence and development.