A horizontally stratified medium consisting of a fluid layer overlaying any number of solid layers is considered. The depth distribution of the density and of the two elastic parameters from prestack offshore surface data is to be determined. The inverse problem is posed in terms of optimization. Its solution is based on nonlinear least squares. Since the solution of the direct problem is an important point in the inversion algorithm, a variational formulation capable of solving the (well-known) numerical difficulty at the liquid-solid interface is used. The acoustoelastic aspect of the problem is stressed. The feasibility of the technique is shown for large-size synthetic examples. It is expected that acoustoelastic inversion will help improve the interpretation of offshore seismic data. >