Extensive laboratory measurements of acoustic wave attenuation in rocks have been carried out in sonic and ultrasonic frequency ranges. Surprising strong ultrasonic shear wave attenuation values, even under high confining pressure, have led us to assume that shear wave birefringence could be responsible for such a behavior. Ultrasonic laboratory measurements of velocity and attenuation of shear waves, as a function of the polarization angle, were performed on a representative water-saturated limestone sample. Experimental results show that attenuation is very dependent on shear wave polarization, since it can be very low along the two principal directions (fast and slow ones) of the sample and much higher elsewhere. By generating synthetic signals from two experimental signals, we have found that, at intermediate polarization angles, the stronger the anisotropy, the stronger the “apparent” attenuation. Agreement between experimental results and theoretical computed ones is quite good.