In this letter, an autonomous spiral stair climbing method for tracked vehicles using the reaction force from side walls has been proposed. Spiral stairs are one of the most difficult terrains for tracked vehicles because of their asymmetrical ground shape and small turning radius. Tracked vehicles are expected to be used in industrial plant inspection tasks, where robots should navigate on multiple floors by ascending the stairs. Spiral or curved stairs are installed as part of inspection passages for cylindrical facilities, such as boilers, chimneys, or large tanks. Previously, the authors have experimentally demonstrated that the wall-following motion is effective for stabilizing and accelerating spiral stair climbing. However, the complete automation of climbing motion or the analysis of why the same motion is generated even if a disturbance exists in the initial entry angle to the wall should be investigated. In this study, the authors developed an autonomous spiral stair climbing method using the wall reaction force and clarified the applicable limitations of this method using a geometrical model. Autonomous spiral stair climbing is realized by attaching passive wheels on its collision point and automating the motions of main tracks and sub-tracks. The geometrical model shows the expected trajectory of the robot on the spiral stairs, which suggests that the robot' s rotation radius converges to a specific value; this is experimentally confirmed by measuring the robot's motion. The wall-following motion of robots is equivalent to human inspectors grasping handrails while climbing stairs. Through collisions with surrounding objects, motion is stabilized and certainty is guaranteed.