This study considers the saturated soil around the tunnel as a transversely isotropic medium and derives the dynamic response solutions of the tunnel lining and its surrounding medium under explosive loads in the Laplace and Fourier transform domains. When the transverse isotropic coefficient equals 1.0, this solution simplifies to the case where the tunnel is surrounded by a uniform medium. By performing inverse Fourier and Laplace transforms on the solution, we obtain the time domain solution. Compared with the results for a uniform medium surrounding the tunnel, it was found that the peak values of stress and pore water pressure increased, while the peak displacement slightly decreased. In addition, the peak arrival time is advanced, and the fluctuation attenuation is accelerated. The transverse isotropy of soil in engineering cannot be ignored.