A non-hydrostatic numerical model is constructed for mesoscale studies,buoyancy equation being introduced into the model to reduce computational error of buoyancy. Control tests to verify the capability of the model to simulate the development and maintenance of the mesoscale circulation processes have been conducted. Characteristic features for generating and maintaining mesoscale systems are shown by the model qualitatively. It is found that. for more complex mesoscale systems, the development of the initial purturbation is related to its dynamical and thermodynamical structures but the maintenance of the systems relies more on the instability of the atmosphere. It is also found that computing stability is sensible to initial conditions.