Preface (V.Maupin, R.S. Wu). 1. Seismic ray method: recent developments (V. Cerveny. L. Klimes, I. Psencik). 2. Introduction to mode coupling methods for surface waves (V. Maupin). 3. Boundary integral equations and boundary elements methods in elastodynamics (M. Bouchon, F. Sanchez-Sesma). 4. Generation and propagation of seismic SH waves in multilayered media with irregular interfaces (X.F. Chen). 5. One-way and one-return approximations (de Wolf approximation) for fast elastic wave modelling in complex media (R.S. Wu, X.B. Xie, X.Y. Wu). 6. Simulation of high-frequency wave propagation in complex crustal waveguides using generalized screen propagators (R.S. Wu, X.Y. Wu, X.B. Xie). 7. Spectral-element analysis in seismology (E. Chaljub, D. Komatitsch, et al.). 8. The finite-difference time-domain method for modeling of seismic wave propagation (P. Moczo, J. Robertson, L. Eisner). 9. A Lattice Boltzmann approach to acoustic-wave propagation (L. Huang). 10. Synthesis of seismogram envelopes in heterogeneous media (H. Sato, M. Fehler).