AB The strain-amplitude and frequency dependencies of compressional- and shear-wave attenuation in siltstone have been experimentally studied. The measurements were performed using the reflection method on pulse frequency of 1 MHz, in the amplitude range 0.3 ≤ epsilon ≤ 2.0 mu strains under constant confining pressure of 10 MPa and ambient temperature. The nonlinear variation of quality factor (Q) depending on the strain-amplitude value (epsilon(min) ↔ epsilon(max)) is detected. The attenuation increment with increasing amplitude takes place only for a certain amplitude-value, further the decrease in attenuation occurs, and the amplitude-dependent peak Q(-1)(epsilon) appears. The relaxation spectrum of the P-wave attenuation Q(P)(-1)(f) has the form of a monotonic curve with steepness which depends on the strain amplitude. The S-wave relaxation spectrum Q(S)(-1)(f) characterizes the presence of a local attenuation peak that tends to vanish with the increase in strain amplitude. Anomalous attenuation behaviour can be explained by the joint action of viscoelastic and microplastic mechanisms. New knowledge can be used for diagnostics of rocks and materials, and the interpretation improvement of acoustical and seismic data