The experiments have been conducted to investigate the effect of strain amplitude and frequency on the compressional and shear wave attenuation in quartz samples of three types: the intact quartz, fractured quartz, and smoky quartz. The measurements were performed using the reflection method on a pulse frequency of 1 MHz with changing strain in the range 0.3 ≤ ≤ 2.0 μstrain under a confining pressure of 10 MPa and at ambient temperature. The essential difference in amplitude-frequency characteristics of wave attenuation in three quartz types has been detected. The intact quartz shows the more “simple” behavior in comparison with the fractured and smoky quartz. The attenuation (the inverse quality factor Q) depends on strain amplitude as Q ⁻¹() ∼ ⁻ⁿ , where n 0.005–0.085, with the greatest decrease in the smoky and fractured quartz reaching of about 15%. Relaxation spectra of attenuation are presented in the frequency range from 0.4 to 1.4 MHz. The dependence Q _p ⁻¹(f) ∼ f ^−1.2 characterizes the intact and fractured quartz, whereas the smoky quartz has the relaxation peak. The dependence Q _s ⁻¹(f) ∼ f ^−0.84 presents S wave relaxation spectrum in the intact quartz; in the fractured and smoky quartz, the attenuation peaks take place. The strain amplitude variation exerts influence on the relaxation strength, the peak frequency, and the width of the relaxation peak. Such behavior of attenuation can be explained by a joint action of viscoelastic and microplastic mechanisms. These results can be considered as a contribution for providing the experimental background to the theory of attenuation in rocks. They can also be used in solving applied problems in material science, seismic prospecting, etc.