The solid texturing technique is used to express grain in computer graphics. However, it cannot currently express the variety of annual tree ring patterns. To solve this issue, we propose an accurate model for the fluctuations of annual ring patterns. We first analyzed the fluctuations of natural pine. Based on this analysis, we designed a fluctuation generation model that combines three elements: disordering of the skeletal axis, disordering of annual ring intervals, and disordering of the circumference. We compared grain texture images created using our fluctuation generation model with images created using the existing method. Our results confirm that the proposed method produced more realistic images.