Tunnel construction commonly causes deformations of the surrounding ground, which can endanger buildings and other structures located in the vicinity of the tunnel. The prediction of these deformations and damages to buildings is difficult, due to limited knowledge of geotechnical conditions and due to uncertainty in predicting the response of the structures to the settlements. This motivates the development of a probabilistic model for the prediction of tunneling-induced damage to buildings. We propose such a model, based on the classical Gaussian profiles for the approximation of the subsidence trough and the equivalent beam method for modeling the response of the building walls. In practice, settlements are commonly monitored through deformation measurements. To account for this, we present a Bayesian method for updating the predicted settlements when measurements are available. Finally, we show how maximum allowable settlements, which are used as threshold values for monitoring of the construction process, can be determined based on reliability-based criteria in combination with measurements. The proposed methodology is applied to a group of masonry buildings affected by the construction of the L9 metro line tunnel in Barcelona.