Tunnels located close to earthquake faults have been damaged during recent earthquakes, and the damage patterns suggest a complex 3D response of the tunnel in these zones. The domain reduction method (DRM) is a computationally efficient finite element method widely used to analyse the response of finite structures to wavefields generated through earthquake fault rupture simulations. However, this method does not work for simulating the seismic response of infinitely long tunnels. In this work, we modify DRM to accommodate infinitely long tunnels. We verify the accuracy of the modification for a wide range of parameters by comparing the numerical solution with existing semi-analytical solutions for the 3D response of tunnels subject to seismic waves incident on the tunnel from arbitrary directions. The boundary effects resulting from the truncation of the soil domain for numerical modelling are also explored, and recommendations on the numerical domain dimensions to ensure accurate results are presented. This modified DRM would be a powerful tool for analysing the 3D seismic response of tunnels subjected to near-fault wavefields generated through earthquake fault rupture scenarios.