Cement grouting is an operation often carried out to consolidate and seal the rock mass in dam sites and tunnels. The quality and efficiency of a grouting operation depends on various factors such as water take, grout properties and grouting pressure. One of the parameters which have the highest effect is pressure since the application of excessive pressure causes the hydraulic fracture phenomenon to occur in the rock mass and too little pressure leads to incomplete grouting and failure to seal the site in a perfect manner. Mathematical modeling is used for the first time in this study to predict and determine the optimum pressure. Thus, the joints that exist in the rock mass are simulated using cylindrical shell model. The joint surroundings are also modeled through Pasternak environment. To obtain equations governing the joints and the surroundings, energy method is used accompanied by Hamilton principle. In the end, an analytical solution method is used to obtain the maximum grouting pressure. In order to validate the modeling, the grouting pressure values obtained by the model were used in the sites of Seymareh and Aghbolagh dams and the relative error rates were measured considering the differences between calculated and actual pressures. Modeling in the examined sections of Seymareh dam showed 29.61, 5.57, 21.98, 32.50 and 9.09 percent error rates and in the sections of Aghbolagh dam it rendered the values of 4.32, 5.40 and 2.96 percent. The results indicate that this modeling can be used to estimate the amount of pressure for hydraulic fracture in grouting, to predict it and to prevent it.