Using the Boussinesq approximation equations for meso-scale disturbances in zonally linear and non-linear shear flows a study is undertaken of the unstable features and wave properties of two typical meso-scale unstable disturbances（i.e.symmetric and transversal instabilities. Results suggest that:1）for symmetric disturbances with its iso-phase plane parallel to the basic flow,the instability of the disturbance is actually the instability of the internal inertial gravity wave propagating in a direction perpendicular to the basic flow.The second-order shear of the basic flow represents an instable factor for the symmetric disturbance,and drives the unstable mesoscale disturbance to travel in the meridional direction;2) for traversal disturbance with its iso-phase plane perpendicular to the basic flow no vortex Rossby wave exists at all when the basic flow is constant or only linearly sheared and the instability of the traversal disturbance is actually the instability of the internal inertial gravity wave propagating simultaneously in two opposite directions with respect to the basic flow.With a second-order or nonlinear vertical shear of the basic flow taken into account,a new kind of wave（vortex Rossby wave） occurs and it propagates in one direction with respect to basic flow₀ and originates physically in the second-order shear of windspeed (β_*=_zz≠0).In fact,the instability of the traversal disturbance may be the instability of mixed vortex Rossby ——gravity wave.In the real atmosphere vortex Rossby wave is crucial to the genesis,development and evolution of meso-β convective cloud nucleus and rain cores.