Underground tunnels are an integral part of modern infrastructure and are used for a wide range of applications worldwide. Seismic response of tunnels is a critical aspect in their design and construction that cannot be ignored for safety evaluation of these structures. In this study, the effects of combined P- (compressional) and S- (shear) waves on three-dimensional (3D) tunnels is investigated using the computationally efficient algorithm, i.e., Domain Reduction Method (DRM), which is a finite element based methodology. The DRM is employed as a numerical tool to efficiently model the seismic behavior of complex structures by dividing them into subdomains, and it allows for accurate simulations with lesser computational costs. Understanding the interaction between P- and S- waves is essential for designing tunnels during seismic loading. The present study focuses on capturing the intricate dynamics associated with these waves and their combined effects on tunnel structures. Parametric analyses for different inclination angles have been carried out to understand the longitudinal and transverse response of these structures. An open-source software, Multiphysics Object-Oriented Simulation Environment (MOOSE) numerical framework, MASTODON (Multi hazard Analysis for STOchastic time-DOmaiN phenomena), is used for the numerical simulation of the underground tunnels. The results reveal the intricate interplay between the P- and S-waves in 3D tunnels, illustrating how the combined effects impact the structural response. The analysis has considered the factors such as tunnel deformations, stress distributions, and potential failure modes under seismic loading. The findings contribute to a deeper understanding of the seismic vulnerability of tunnels, aiding the engineers and designers in developing robust underground facilities capable of withstanding the diverse seismic scenarios.