Abstract: By using the system of 3D dynamic equations for small-and meso-scale disturbances the series investigation is performed of obliquely crossing instability of zonal line-like disturbance moving at an arbitrary angle with basic flow, arriving at the results as follows: (1) with linear shear available, the obliquely crossing instability of disturbances will occur only when the flow shearing happens in the direction along or perpendicular to the line-like disturbance movement, with the obliquely crossing instability showing the instability of internal inertial gravity waves; (2) in the presence of second order non-linear shear the disturbance of obliquely crossing instability includes internal inertial gravity and vortex Rossby waves. For the zonal line form disturbance under study, the vortex Rossby wave has its source in the second shear of meridional wind speed in the flow and propagates unidirectionally with respect to. As meso-scale obliquely crossing unstable disturbances, the vortex Rossby wave has its origin from the second shear of the flow in the direction vertical to line-form disturbance and is independent of the condition in the direction parallel to the flow; (3) for general zonal line like disturbances, if the second shear happens in meridional wind speed , i.e., the second shear of the flow in the direction perpendicular to the line-form disturbance, then the obliquely crossing instability of disturbances is likely to be the instability of mixed Vortex Rossbyinternal inertial gravity waves. Finally, we have simulated the rainstorm process in the Fujian Province in the June of 2006 by use of the WRF model to verify the foregoing theoretical results. By analysing the vertical profile of the averaged U over the precipitation area at 13:00 BST June 6, 2006, it is found that in the atmosphere between 950 and 100 hPa, the zonal wind U had the second order shear with altitude, with the small speed in lower and upper troposphere, and the larger speed in middle troposphere near the 400 hPa. In such a circumstance, the second order derivative of the averaged zonal wind U with respect to altitude was not zero, and therefore triggered the vortex Rossby Waves, which played an important role in the moving of the β meso-scale rain cluster in the heavy rainfall area. By analyzing the meridional variation of 850 hPa and 500 hPa averaged zonal winds over the precipitation area both at 23:00 BST June 5 and at 13:00 BST June 6, it is found that there existed the second-order meridional shear of the averaged zonal wind both on June 5 and June 6 at 850 hPa, but at 500 hPa there only existed the linear meridional shear instead of the second meridional shear. The analysis indicate that it's easy to produce the vortex Rossby waves in the lower troposphere, but difficult in the middle and upper troposphere since not having condition producing vortex Rossby waves, implying the waves there are solely internal inertia gravity waves.