Sichuan Basin is located in the eastern margin of Qinghai-Tibet Plateau, with frequent earthquakes. The dynamics of red-bed rocks widely distributed in this area is an important factor affecting the long-term safety of many major projects construction and operation. Therefore, in this paper, a series of uniaxial cyclic loading and unloading tests with different dynamic stress amplitudes were carried out on the three typical red bed sand and mudstones (silty mudstone, argillaceous siltstone and fine sandstone). The results show that: under the same dynamic stress amplitude, the relative area of hysteresis loop, damping ratio and damping coefficient of the silty mudstone and fine sandstone and that of the argillaceous siltstone decrease logarithmically with the cycle times, while the damping coefficient of the argillaceous siltstone shows an open downward quadratic polynomial distribution with the cycle times. In the same cycle, the relative area of hysteresis loop increases exponentially with the increase of stress amplitude, the damping ratio of silty mudstone and argillaceous siltstone increases exponentially, the damping coefficient is a quadratic polynomial distribution in the downward direction of the opening, and the damping ratio and damping coefficient of fine sandstone are logarithmic decreasing.