Abstract We propose a time-domain matrix-free elastic Gauss-Newton fullwaveform inversion (FWI) algorithm. At the core of our elastic Gauss- Newton FWI is an iterative elastic least-squares reverse time migration (LSRTM) problem. The proposed algorithm consists of two nested iteration loops: the outer Gauss-Newton nonlinear iterations and the inner conjugate gradient least-squares (CGLS) iterations. The Gauss- Newton search direction in each outer FWI iteration is computed using the CGLS method. This step is equivalent to applying elastic LSRTM on data residuals. We use the proposed algorithm to simultaneously invert for P- and S-wave velocities. The algorithm retrieves moderately improved models than the nonlinear conjugate gradient (NLCG) method. We observe that the elastic Gauss-Newton FWI converges faster than the elastic NLCG FWI. Presentation Date: Wednesday, October 17, 2018 Start Time: 1:50:00 PM Location: 207C (Anaheim Convention Center) Presentation Type: Oral.