Bridge and crossing high-speed train represent an uncertain interacting dynamic system of high complexity with, in general, time-dependent system matrices. Thus, full reliability assessment of this system can only be conducted efficiently in an interdisciplinary approach, bringing together the disciplines of structural mechanics, engineering mathematics, and high performance computing. This contribution gives a brief summary on computational modeling issues of uncertain bridge-train interaction, its efficient stochastic simulation, and an outline of pros and cons of different strategies is provided.This is an open access article under the terms of the Creative Commons Attribution-Non-Commercial-NoDerivs Licence 4.0, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.