A rigorous theoretical foundation for solving elastodynamic inverse problem of multilayered media under an impulse load is established in this paper. The inversion is built upon the forward dynamic analysis of multilayered elastic media using transfer matrix approach, with which displacement continuity is assumed at the interfaces of upper and lower adjacent layers. Formulations for inverse analysis are derived in both the time domain and the complex frequency domain. Least square estimates and nonlinear optimization algorithms are used to implement parameter identification. The proposed theory and formulae can be utilized to develop a computer software for nondestructive evaluation of laminated civil and aerospace structure (highway and airport pavements, bridge decks, soil foundations, aircraft wing, etc.), exploration and dynamic source detection and identification, and petroleum exploration in geophysics.