Disaster response robots are important for the investigation of nuclear power and chemical plants. To investigate an area, robots are required to climb straight or spiral staircases because equipment components are installed on different-level floors, which are connected by stairs. Installed stairs are narrow and steep because the location of equipment components is given priority in the environment inside plants. It is considerably difficult for a tracked vehicle, which has high mobility on stairs or rough terrain, to climb spiral staircases. We propose a method for a tracked vehicle to climb spiral staircases. A characteristic of the method is that the tracked vehicle uses the reaction force from a safety wall, which is installed to prevent objects from dropping down and damaging the equipment in plants. It is shown that the climbing motion is easy to perform using the wall without complicated control, as compared to when the wall is not used. The climbing motion of a robot on a spiral staircase using a wall is analyzed by employing a dynamic model. Experimental results show that it is possible to climb without slippage and at a high speed by maintaining contact along the wall. These results show that a tracked vehicle can access areas that could not be reached earlier through contact with the environment. Furthermore, it is considered that the climbing motion using contact with the environment can be applied to an autonomous mobile robot for automating inspection because complicated control is not required.