Abstract: The numerical methods for inverse problems in elastic dynamics are introduced in this paper. These methods include linear inverse methods under some approximation, non-linear iterative inverse methods in time domain or in frequency domain, optimizing method with deterministic or non-deterministic searching in the solution space, homotopy methods that converge in a large domain and multi-scale inverse methods composed of multigrid and wavelets. The principle, characteristics and limits of thes emethods are analyzed and the further research of numerical inverse methods in the future are discussed.