Soundproof equations do not contain acoustic waves,which is why numerical models based on soundproof equations can use relatively lager timesteps for numerical integration.Durran proposed a new method to eliminate acoustic waves in 1989 and named it "pseudo-incompressible" equations,which retain the air density variations caused by temperature perturbations but ignore the density variations caused by pressure perturbations.In this paper,the authors followed the pseudo-incompressible theory and derived a set of flux-form pseudo-incompressible equations in the terrain-following coordinate.The form of the set of equations the authors derived is quite similar to that of the equations in the ARW (Advanced Research WRF) dynamic solver of the WRF (Weather Research and Forecasting) model.The authors further modified the codes of WRF model according to the flux-form pseudo-incompressible equations,and thus established the "pseudo-incompressible model" based on the frame of WRF model.The authors then conducted two sets of numerical experiments,i.e.a heat-bubble convection experiment and a gravity current experiment,using the pseudo-incompressible model and WRF model,respectively.Comparing the results of these simulations,the authors found that the meteorological fields simulated by the pseudo-incompressible model are quite close to those by the WRF model,which indicates that the pseudo-incompressible model we built within the frame of WRF model is reliable.