The relation between thermal expansion coefficient and grain-boundary crack volume of aluminium titanate ceramics has been calculated based on the thermal expansion data of a single crystal. The calculation began with the drawing of a frequency distribution curve of the thermal expansion coefficient for a single grain. Using the single-grain distribution curve, a distribution cu rye of an average coefficient for two adjacent grains was derived. The thermal expansion with a partially grain-boundary cracked body was calculated in relation to the amount of cracked boundary from the average distribution curves. The expected relation between crack volume and thermal expansion was close to that of the experimental data.