PURPOSES : Thermal cracking (also called low-temperature cracking) is a serious stress for asphalt pavement, especially in eastern South Korea, the northern USA, and Canada. Thermal cracking occurs when the level of thermal stress exceeds the corresponding level of low temperature strength of the given asphalt materials. Therefore, computation of thermal stress is a key factor for understanding, quantifying, and evaluating the level of low-temperature cracking resistance of asphalt pavement. In this paper, two different approaches for computing thermal stress on asphalt binder were introduced: Hopkins and Hamming’s algorithm (1967) and the application of a simple power-law function. All the computed results were compared visually; then the findings and recommendations were discussed. METHODS: Thermal stress of the tested asphalt binder was computed based on the methodology introduced in previous literatures related to viscoelastic theory. To perform the numerical analysis, MATLABTM 2D matrix-correlation and Microsoft Excel visual basic code were developed and used for the function fitting and value-minimization processes, respectively. RESULTS : Different results from thermal stress were observed with application of different computation approaches. This variation of the data trends could be recognized not only visually but also statistically. CONCLUSIONS: It can be concluded that these two different computation approaches can successfully provide upper and lower limits (i.e. boundaries) for thermal stress prediction of a given asphalt binder. Based on these findings, more reliable and reasonable thermal stress results could be provided and finally, better pavement performance predictions could also be expected.