The occurrence of gas hydrate or free gas in a porous medium changes the medium"s elastic properties. Explicit formulas for gas-hydrate or free-gas saturation of pore space on the basis of the Frenkel-Gassmann equations describe the elastic moduli and seismic velocities of a porous medium for low frequencies. A key assumption of the model is that either gas hydrate or free gas is present in the pore space in addition to water. Under this assumption, the method uses measured P- and S-wave velocities and bulk density along with estimates of the moduli and densities of the solid and fluid phases present to determine whether gas or hydrate is present. The method then determines the saturation level of either the gas or the hydrate. I apply the method to published velocity and density data from seismic studies at the antarctic Shetland margin and at the Storegga slide, offshore Norway, and to borehole log and core data from Ocean Drilling Program (ODP) Leg 164 at Blake Ridge, offshore South Carolina. A sensitivity analysis reveals that the standard deviations of the gas-hydrate and free-gas saturations reach 30%-70% of the saturations if the standard deviations of the P- and S-wave velocities and of the bulk density are 50 ms and 0.05 g/cm (super 3) , respectively. I conclude that a reliable quantification of gas hydrate and free gas can be achieved by seismic methods only if the seismic velocities and bulk density of the medium are determined with high accuracy from the measured data.