The analysis of seismic ground surface response in the presence of underground structures, particularly in anisotropic media, is a significant topic in earthquake engineering and the design of underground structures. This study aims to develop a numerical model for analyzing the seismic ground surface response induced by twin lined horseshoe-shaped tunnels embedded in an orthotropic half-space subjected to vertically propagating SH waves. The surrounding soil and tunnel linings are assumed to represent dense sand and concrete, respectively, while the ground is modeled as a linear elastic orthotropic medium. To this end, a time-domain half-space boundary element method is developed and validated against available benchmark solutions. Subsequently, the effects of key parameters, including the isotropy factor, the horizontal spacing between the tunnels, and the frequency content of the incident wave, on the seismic ground surface response are investigated. The results indicate that decreasing the isotropy factor leads to more complex wave propagation and interference patterns at the ground surface, whereas increasing the horizontal spacing between the tunnels reduces the intensity of their dynamic interaction. In addition, the ground surface response exhibits a pronounced dependence on the frequency content of the incident wave. The proposed model provides an efficient numerical tool for the seismic analysis and design of twin tunnels and other underground structures embedded in anisotropic media.