Symmetric instability is analytically investigated of the right side of upper air jet entrence region and the left side of lower level jet entrance region with non-thermal wind gradients available in the context of a ƒ-plane, non-hydrostatic equilibrium and acoustic wave filtering model for meso-scale research purposes, arriving at an analytic expression of perturbation streamfunction, whereby qualitative analysis is done of the existence of non-thermal gradients, meso perturbation wave structure and spatial distrbution features of wave amplitude. And obtained analytically are the disturbance half wave-length L_c and criterion for symmetric instability with non thermal gradients available. Results presented can account for causes of vigorous rainstorm genesis at jet entrance regions one atop the other at high-and lower levels.