This paper presents the results of experiments on the effect of variable amplitude and pressure on the P-wave velocity and attenuation in cemented sandstone sample. The measurements were performed in transmitted waves at a predominant pulse frequency of 6.8 kHz in the range of strain amplitudes Aε ≈ (0.2−2.4) × 10−6 at an axial static pressure of 0.25 MPa to 1.0 MPa. The wave velocity depends weakly on the amplitude and decreases only slightly with its increase. With increasing pressure the velocity Ve nonlinearly increases (to 6%) at all amplitudes. The attenuation increases linearly (to 2.5%) with increasing amplitude and decreases nonlinearly with increasing pressure. There is an anomalous change in the attenuation in the pressure range (0.5–0.75) MPa, where it decreases to 30% at all amplitudes. These results may be useful for improving acoustic and seismic methods of diagnostics.