This paper presents a simplified procedure to perform probabilistic analysis of responses induced by tunnelling perpendicularly beneath an existing tunnel. Numerical package FLAC3D (Itasca, 2017) was adopted to carry out a series of extensive parameter studies of crossing tunnels based on the orthogonal test design. Subsequently, two closed-formed limit state functions have been developed via the logarithmic regression to estimate the global factor of safety as well as the induced maximum settlement of the existing tunnel. The predicted values of the two state functions were in good agreement with the field data from case histories. The developed surrogate models were implemented into the Excel First-Order Reliability Method (FORM) spreadsheet to calculate the ultimate limit state failure and the probability that the threshold maximum settlement value is exceeded. The FORM results were also validated by the Monte Carlo Simulation. This proposed method is an effective way to evaluate the safety and serviceability of tunnelling perpendicularly beneath an existing tunnel.