In recent decades, construction of urban and suburban tunnels has become very important in order to reduce urban pollution, conserve fossil fuels, reducing travel distances and energy costs. Among tunnel excavation methods, the application of mechanized excavation techniques is increasing by technology advances. One of mechanized excavation methods is excavation by tunnel boring machines (TBMs). In tunnel boring machines, the prediction of machine performance is a very important and critical issue, because it is affected by mechanical parameters of machines, geological parameters and operational parameters. In this research, first penetration rate of TBM open type applied in Queens Tunnel of New York is predicted by mathematical equation. Then, the influence of uncertainty on this parameter is simulated, using the Monte Carlo stochastic modeling and the mathematical relation obtained from the previous step. For this purpose, data such as rock brittleness index, distance between plane of weakness, angle between plane of weakness and TBM-driven direction, excavation specific energy, thrust force, cutterhead power and cutterhead torque, were used to predict the measured penetration rate. One of the problems in this study was the high correlation between input data, which caused a multicollinearity problem. This problem creates the marginal effect of input data on each other and reduces the accuracy and efficiency of mathematical model. In order to solve this problem and reduce the amount of input data, software and principal component's analysis (PCA) were used. Applying the principal component's analysis on the input data, four main components were obtained and by performing a linear regression between the penetration rate (The dependent variable) and these four components, a relationship was found for penetration rate prediction. In the next step, data distribution functions were obtained and entered into the @Risk software to investigate the effect of uncertainty on the penetration rate index. The results showed that along the tunnel route, increasing parameters like brittleness index, angle between plane of weakness and TBM-driven direction, cutterhead power and cutterhead torque, led to increase in penetration rate and with increasing parameters like distance between plane of weakness, excavation specific energy and thrust force has a negative impact on penetration rates. Furthermore, the sensitivity analysis of the penetration rate and impact of input parameters on it were also analyzed, it was found that the brittleness index with a correlation coefficient of +0/528 and the thrust force with -0/0117 value have the most effective and the least effective role on controlling the penetration rate.