We estimate the elastic properties of marine sediments beneath the seabed by means of high‐resolution velocity analysis and one‐dimensional elastic full‐waveform inversion performed on two‐dimensional broad‐band seismic data of a well‐site survey. A high‐resolution velocity function is employed to exploit the broad frequency band of the data and to derive the P‐wave velocity field with a high degree of accuracy. To derive a complete elastic characterisation in terms of P‐wave and S‐wave velocities (Vp, Vs) and density of the subsurface, and to increase the resolution of the Vp estimates, we apply a one‐dimensional elastic full‐waveform inversion in which the outcomes derived from the velocity analysis are used as a priori information to define the Vp search range. The one‐dimensional inversion is done using genetic algorithm as the optimisation method. It is performed by considering two misfit functions: the first uses the entire waveform to compute the misfit between modelled and observed seismograms, and the second considers the envelope of the seismograms, thus relaxing the requirement of an exact estimation of the wavelet phase. The full‐waveform inversion and the high‐resolution velocity analysis yield comparable Vp profiles, but the full‐waveform inversion reconstruction is much more detailed. Regarding the full‐waveform inversion results, the final depth models of P‐ and S‐wave velocities and density show a fine‐layered structure with a significant increase in velocities and density at shallow depth, which may indicate the presence of a consolidated layer. The very similar velocities and density‐depth trends obtained by employing the two different misfit functions increase our confidence in the reliability of the predicted subsurface models.