It is widely known that many traffic accidents occur every year not only in Japan but also throughout the world. Sleepiness or drowsiness, which is the cause of dozing at the wheel, happens regardless of the physical condition of the driver at the time such as after having had meals or at midnight. This indicates that it is too difficult to expect the driver to avoid sleepiness or drowsiness by themselves. Therefore, various systems have been proposed to prevent traffic accidents caused by dozing at the wheel. In this study, we examined the relationship between subjective sleepiness during driving, which was evaluated by the Japanese version of the Karolinska sleepiness scale (KSS-J) and physiological parameters extracted from thoracic respiration signals. Then we tried to classify the existence of heavy, light, and no sleepiness using a support vector machine on those parameters. In this study, we determined a KSS-J score of 8 or 9, 6 to 8, and from 1 to 5 as signifying heavy, light, and no sleepiness states. The support vector machine was trained using three-quarters of the data for each subject and the remaining data was used as the testing data. This approach enabled us to obtain an accuracy of 89.4%. Therefore, it was suggested that thoracic respiration parameters were relevant to sleepiness.