Based on the fundamental solutions due to Dirac's d function for transversely isotropic media, a numerical scheme for wave propagation in two-dimensional orthotropic media is developed within the boundary element method in the time domain. Criteria for selection of the time and space discretizations for convergent and accurate results are established. The applicability and accuracy of the scheme are verified by a number of benchmark problems including dynamic responses of an orthotropic half plane under uniform harmonic surface loadings and a circular cavern in slightly orthotropic media under the incidence of pseudo-P and-SV waves. The procedure is then applied to examine wave propagation for an underground tunnel with different ratios of orthotropy in the media. The effects of different wave parameters and ratios of orthotropy on dynamic response of the tunnel are presented.