Gas hydrates occur within sediments on the western Svalbard continental margin and the Vestnesa Ridge, a large sediment drift that extends in a west-northwest direction from the margin toward the mid-ocean ridge. We acquired multicomponent ocean-bottom seismic (OBS) data at 10 locations on the crest area of the eastern segment of the Vestnesa Ridge, an area with active gas seepage. P and S wave velocities are estimated using traveltime inversion, and self-consistent approximation/differential effective medium rock physics modeling is used to estimate gas hydrate and free gas saturation at OBS stations. We apply 1-D full waveform inversion at a selected OBS station to study detailed variations of P wave velocity near the bottom simulating reflection (BSR). High interval P wave velocity (Vp ≈ 1.73-1.82 km/s) and S wave velocity (>0.35 km/s) are observed in a layer above the BSR and low interval P wave velocity (Vp ≈ 1.28-1.53 km/s) in a layer below the BSR. We estimate 10-18% gas hydrate and 1.5-4.1% free gas saturation at different OBS stations in a layer above and below the BSR, respectively. We find significant variation in gas hydrate and free gas saturation across faults suggesting a structural control on the distribution of gas hydrate and free gas in the Vestnesa Ridge. Differences in gas hydrate saturation derived from P wave velocities and earlier estimates obtained from electromagnetic surveys indicate the presence of gas hydrates in faults and fractures. Moreover, beneath some OBS sites, the combined study of P and S waves, resistivity and seismic quality factor (Q), suggests the coexistence of free gas and gas hydrates.