We develop an inverse method with the purpose of extracting elastic properties of materials in the framework of transient dynamics. To this end, we create a small linear system based on a set of well-chosen time-dependent virtual fields (VF) and measurement data. The parameters are the solutions of this system and can be quickly extracted. We compare this new method with the classical finite element model updating (FEMU) method for different case studies. In our study, the measurements are synthetic, i.e, they are calculated using a fine finite element (FE) model. Uniform white noise is added to model measurement uncertainties. Results, based on Monte Carlo simulations, show that our method is more robust and accurate than the FEMU method for an acceptable noise level. Our new method appears well-adapted to linear elasticity in transient dynamics.