A significant portion of the world's hydrocarbon reserves are found in carbonate reservoirs, yet analysis of the petrophysical properties of these reservoirs is associated with a number of challenges. Some of these challenges stem from physical and chemical interactions between the carbonate rock matrix and pore fluids, which can affect elastic properties of the rock. Hence, the study of the pore fluid effects on the elastic properties of carbonates is important for understanding a change of the field performance properties of а carbonate reservoir caused by fluid movements during hydrocarbon extraction in producing fields. In this laboratory study, we investigate the applicability of Gassmann's model for predictions of the elastic moduli of water‐ and hydrocarbon‐saturated Savonnières limestone and the influence of partial water saturation on elastic and anelastic properties of the rock. We present the results of two sets of laboratory experiments on the Savonnières oolitic limestone where we: (i) evaluate the effect of full water and n‐decane saturation on elastic moduli and attenuation at seismic (0.1 Hz–120 Hz) and ultrasonic (0.5 MHz) frequencies; and (ii) quantify the dependence of elastic moduli and extensional attenuation on water saturation at two seismic frequencies of 1 Hz and 10 Hz. We demonstrate that the change in the bulk modulus of limestone fully saturated either with n‐decane or water is in agreement with Gassmann's fluid substitution theory, whereas the shear modulus is noticeably reduced. The measurements with partial saturation show that the bulk modulus decreases with increasing water saturation to a lesser extent than the Young's and shear moduli. Our results show that extensional attenuation in the samples with closed boundaries is insignificant under dry and fully saturated conditions but is influenced greatly by the liquid content when saturation is between 0 and 20% or 95% and 100%.