One of the most important parameters used for determining the performance of tunnel boring machines (TBMs) is their penetration rate. The parameters affecting the penetration rate can be divided in two categories. The first category is the controllable parameters such as the TBM technical characteristics, and type and geometry of the tunnel, and the second one is the uncontrollable parameters such as the intact rock properties and characteristics of the rock mass discontinuities. The aim of this work was to investigate the effects of rock mass properties on the penetration rate, and to present a new mathematical equation based on a statistical approach to estimate the TBM performance. To achieve this aim, the Monte-Carlo (MC) simulation method was used to model the TBM performance. Accordingly, the database consisting of the rock mechanics information such as the uniaxial compressive strength, Brazilian tensile strength, toughness and hardness of rock, spacing and orientation of discontinuities, and measured TBM penetration rate in 151 points out of a water tunnel was collected. Next, using the dimensional analysis, a comprehensive mathematical equation was obtained to calculate the TBM penetration rates using the developed database. Finally, using the MC simulation method, the probability distribution function of the TBM penetration rate was studied. The validation results obtained showed that the root mean square error (RMSE) of the proposed relationship was less than 0.3. The MC simulation results showed that hardness and density had the most and least effects on the penetration rate, respectively.