A mathematical model is established to predict the salt cavern development during leaching in high-insoluble salt formations. The salt-brine mass transfer rate is introduced, and the effects of the insoluble sediments on the development of the cavern are included. Considering the salt mass conservation in the cavern, the couple equations of the cavern shape, brine concentration and brine velocity are derived. According to the falling and accumulating rules of the insoluble particles, the governing equations of the insoluble sediments are deduced. A computer program using VC++ language is developed to obtain the numerical solution of these equations. To verify the proposed model, the leaching processes of two salt caverns of Jintan underground gas storage are simulated by the program, using the actual geological and technological parameters. The same simulation is performed by the current mainstream leaching software in China. The simulation results of the two programs are compared with the available field data. It shows that the proposed software is more accurate on the shape prediction of the cavern bottom and roof, which demonstrates the reliability and applicability of the model.