Samples of shales from the Ordovician Bongabinni and Goldwyer source rock formations were recovered from the Canning Basin (Western Australia). Attenuation was experimentally measured on preserved plugs from these formations in the frequency range between 10−2 and 102 Hz. Samples cored with different orientations with respect to the sedimentary bedding were prepared and tested in their native saturated state and after drying in the oven at 105 °C for 24 hr to assess the effect of fluids and of the sediment anisotropy on attenuation. To aid the interpretation of the experimental results, the clay-rich samples were characterized in terms of mineralogy, water content, porosity, permeability and microstructure. The two shales have significantly different quality factors; and this is seen to be dependent on both the saturation state of the samples and the propagation direction of the oscillatory signal. The attenuation coefficient for compression/extension parallel to bedding is less than that vertical to bedding in both the preserved and partially dehydrated situations. No frequency dependency is observed in the preserved samples within the range of frequencies explored in this study. On the other hand partially saturated samples show peaks in attenuation at around 40 Hz when the stress perturbation is transmitted normal to the macroscopic bedding. The interpretation of the attenuation measurements in terms of well-established theoretical models is discussed in view of the physical characteristics and microstructure of the tested rock