Extensional and torsional wave‐attenuation measurements are obtained at a sonic frequency around 1 kHz on partially saturated limestones using large resonant bars, 1 m long. To study the influence of the fluid distribution, we use two different saturation methods: drying and depressurization. When water saturation (Sw) is higher than 70%, the extensional wave attenuation is found to depend on whether the resonant bar is jacketed. This can be interpreted as the Biot‐Gardner‐White effect. The experimental results obtained on jacketed samples show that, during a drying experiment, extensional wave attenuation is influenced strongly by the fluid content when Sw is between approximately 60% and 100%. This sensitivity to fluid saturation vanishes when saturation is obtained through depressurization. Using a computer‐assisted tomographic (CT) scan, we found that, during depressurization, the fluid distribution is homogeneous at the millimetric scale at all saturations. In contrast, during drying, heterogeneous saturation was observed at high water‐saturation levels. Thus, we interpret the dependence of the extensional wave attenuation upon the saturation method as principally caused by a fluid distribution effect. Torsional attenuation shows no sensitivity to fluid saturation for Sw between 5% and 100%.