Abstract: Abstract: This study introduces the multistage scheme incorporating with an irregular shortest path method (ISPM) for tracking multiple arrivals composed of any kind of combinations of transmissions, conversions and reflections in complex 2D/3D layered media. The principle is first to divide the layered model into several different computational domains using irregular cells at the interface and the Earthrsquo;s undulated surface, and then to apply the multistage technique to trace the multiple arrivals. It is possible to realize the multiple arrival tracking with the multistage technique, because the multiple arrivals are different combinations or conjugations of the simple incident, transmitted and reflected waves via the velocity discontinuities. Benchmark tests against the multistagefast marching method （FMM） are undertaken to assess the solution accuracy and the computational efficiency. The results show that the multistage ISPM method is advantageous over FMM method in both solution accuracy and CPU times.