In rock physics, much attention has been paid to the study of the processes of strain of natural materials at small strains. Experiments using high-precision measurements have allowed new knowledge at micro/nano level to be acquired. The microplasticity of solids is studied in materials science, but there is also data regarding some rocks. The property of microplasticity of natural materials is still little studied. The study was carried out on rock samples. The effect of strain amplitude and confining pressure on the velocity and attenuation of P and S waves in dry and water-saturated sandstone has been studied. The method of reflected waves was used in the frequency range of 0.5-1.4 MHz at four strain amplitudes (0.5-1.67) · 10^-6. Amplitude cycling causes an open and closed hysteresis effect for wave velocity and attenuation. This has been observed for both dry and water-saturated sandstone. The hysteresis loop overlaps in both states. The amplitude changes in the velocity of P-wave in dry sandstone is 1.12 %, and the attenuation of P-wave in dry sandstone is 5.43 %. As for S-wave, its maximum attenuation in dry sandstone reaches 8.81  %. The behavior of a wave velocity and attenuation can be explained by the combined effect of viscoelasticity and microplasticity. Elastoplastic transition strongly depends on the details of the microstructure, its defectiveness, and other parameters. The characteristics of  the complications of wave parameters can be the signs of the internal structure of the subject.