Abstract: The object of mesoscale meteorological research is the atmospheric phenomena, to which the geostrophic balance similarity can not be applied, but the the hydrostatic balance similarity still can be applied. The range of its horizontal scale is about 2.5 to 2500 km. The numerical model for the mesoscale meteorological research should have such features as: high horizontal resolution, description of underlying surface with high precision and high resolution, detailed parameterization of physical processes, utmost reduction of the reflection of gravity wave onupper and lateral boundaries. lower boundary conditions coinciding with real situations and compressible(at least anelastic) mass continuity equation. A mesoscale me-teorological numerical model, which possesses the features mentioned above, is simply intro-duced in this paper including: basic equations, parameterization of physical processes, boundary condi-tions and numerical integration methods.

Key words: mesoscale meteorology, mesoscale meteorological numerical model