Abstract: In order to consider both the thermal stress accumulation and relaxation effects of asphalt concrete (AC) during the process of temperature drop, and determine the critical cracking temperature, the low temperature shrinkage coefficient tests were conducted on AC specimens, and the tensile strength and creep compliance were determined from indirect tensile tests. The Prony series representation of relaxation modulus was obtained from the theoretical relationship. The thermal stress was computed according to the Boltzmann superposition principle. Thermal stresses induced at several of temperature drop rates were analyzed and the critical cracking temperatures (CCT) were determined based on the tensile strength curve. The calculation results were verified. The results show that this approach can take both the stress accumulation and relaxation into consideration, and better represent the low temperature cracking characteristic of AC. The calculation results are similar to that obtained from thermal stress restrained specimen test (TSRST). This approach can apply to both uniform temperatures drop and continuous drop in the field. The rate of thermal stress accumulation increases with decreasing temperature or increasing drop rate. The CCT increases with increasing drop rate.