Abstract: The tests on the uniaxial compression of concrete specmens have been done under the conditions of different loading rates (10-5/s,10-4/s,10-3/s,10-2/s) in this study. Based on the improved Weibull model an expression for the damage variables was set up, and the further detailed researches on the damage curves under the strain space were carried out yet. According to the characteristics of the damage curves, the establishment of a reasonable method to determine the positions of the damage critical points on the curves, and then through two damage critical points the curves are divided into three stages. On this basis, the influences of the damage critical points and the length of the stages under the different loading rates were analysed. The test analysis results show that: (1) the first damage critical point is more sensitive to the increase of the loading rates and is almost linear development process with the increase of the loading rates, the second damage critical point is not sensitive to the increase of the loading rates. (2) the increase in the loading rates made the redistribution of the interval length of the three damage stages, which has the greater influences on the first two stages and no influences on the interval length of the third stage. (3) the positions of two damage critical points are symmetrically distributed on the both sides of the peak strain, and the most of the damage is focused within the peak strain about twice as large as the peak stress, and the ratio of the stress level corresponding to two damage critical points is about 3.5 and it decreases with the increase of the loading rates.