The current study is an attempt to address the stochastic nature of the rock excavation process by suggesting a stochastic performance prediction model implemented into a deterministic model developed for hard rock TBMs. Full-scale linear cutting experiments using constant cross-section and V-type of disc cutters are performed on two different limestone samples to provide the basic input required for the deterministic model used for estimation of instantaneous penetration rate, daily advance rate, thrust and torque requirements of TBMs. Stochastic estimation is performed by using a Monte Carlo simulation program by applying iterations to implement the probabilistic distribution of each model parameter and provide knowledge of a confidence level. Results of the suggested model are verified by measuring the field performance of two earth pressure balance (EPB) TBMs excavating competent rocks in semi-closed mode. The results indicate that the suggested model works well for prediction of instantaneous cutting/penetration rate for both TBMs and both types of disc cutters. However, an improvement on the model is required for estimation of cutterhead torque and thrust of EPB TBMs. The stochastic model implemented into the deterministic model results in almost similar predictions with the deterministic model in 50% (best guess) probability. However, the stochastic modeling provides a tool for exploring the full implications of linear cutting experiments and allows assessing the probability of occurrence and predicting variations of the TBM performance parameters, covering the uncertainties/risks. (C) 2014 Elsevier Ltd. All rights reserved.