Abstract: In order to study the dynamic mechanical properties of northwest artificial frozen red sandstone,the shock compression tests were conducted on red sandstone at -15 ℃ using SHPB apparatus. In the SHPB tests,five groups of valid test data were analyzed,and five stress-strain curves were obtained with different average strain rates. Based on the damage evolution and the component model theory,the frozen red sandstone is considered as a non-uniform particle composed of elastic,damage,plastic and viscous properties. In this paper,a time dependent damage model which in- cludes the damaged body element,the clay pot and the spring is established. It is found that the strength of the speci- men is exponentially correlated with the average strain rate. When the average strain rate is low,the strength of the specimen changes gently,and the strength of the specimen increases sharply at the high average strain rate. When the average strain rate is 120. 73 s-1 ,the peak value of stress is as high as 84. 96 MPa,which is about twice of the static compressive strength of 44. 1 MPa. The time dependent damage model can reflect the stress-strain relationship of the frozen red sandstone in a certain range.