Abstract: The short-range numerical weather prediction model has been developed as a tool to forecast the torrential rainfall since it has the capability to describe the dynamic convergence, fundamental physics and the real topography reasonably when the horizontal resolution is increased to a few tens of kilometers. The nearly fifty years of development in the meso-scale numerical prediction model for heavy rainfall has witnessed great changes in the dynamical core from hydrostatic to non-hydrostatic, the resolution from coarse to fine, the physical processes from simple to comprehensive, cloud and precipitation forecast from implicit to explicit and initialization from simple interpolation to complicated assimilation. In this paper, we mainly focus on dynamical frames, physical packages and initialization techniques of the meso-scale numerical heavy rainfall prediction model to analyze its important advances at home and abroad. Some future directions of the model development are also suggested. The review will be helpful to understand the current status and development trend of meso-scale model as an important tool to study and forecast heavy rainfall.