The article studies velocities of P-waves and S-waves in a natural sandstone specimen exposed to axial thrust. The cylindrical core specimen 1 m long and 0.08 m in diameter is composed of different size blocks. Anomalous velocities of the P-waves and S-waves (4-6 kHz) have been revealed by measurements in the whole specimen, in it separate blocks and at contacts surfaces between the blocks. The velocities in the whole specimen are much smaller than in its separate blocks. The interblock contacts detain and decelerate the waves. With smaller spacing at the contacts between the blocks, the wave velocities linearly drop to anomalously low vales (hundreds m/s)
