The masoscale WRF model is used to simulate Typhoon Matsa that occurred over the western North Pacific in August 2005.The simulation data are applied to a barotropic shallow water equation to study the barotropic characteristic wave structures and their stabilities when Matsa reaches its peak.The results show that there are counterclockwise-propagating external inertial-gravity waves and vortex Rossby waves inside Matsa,which have different structures and stabilities.The external inertial-gravity waves occur the outer part of Matsa,and their growth rate increases as wavelength reduces,and the wave phase speed over the outer part is 48.9-68.5 m·s^-1.The Rossby waves appear over the 200 km of center area,and their wave number-3 is the most unstable,with 5 m·s^-1 phase speed at the 100 km radius.In addition,the perturbation wind fields of the external inertial-gravity waves are generally perpendicular to the height fields,and the ratio of perturbed divergence to perturbed vorticity is over 3 and could be up to 10³,indicating that the waves are associated with divergence.The perturbed wind fields of the Rossby waves are generally parallel to the height fields,the ratio of perturbed divergence to perturbed vorticity is 10^-1-10^-2,and the waves are related to vorticity,which is intimately associated with tangential propagation of spiral rainbands.