The integration of self-driving vehicles may expose individuals with health concerns to undue amounts of stress. Psychophysiological indicators of stress were used to determine changes in tonic and phasic stress levels brought about by a high-fidelity autonomous vehicle simulation. Twenty-eight participants completed one manual driving task and two automated driving tasks. Participants reported their subjective level of trust in the automated systems using the Automation Trust Survey. Psychophysiological stress was indexed using skin conductance and trapezius muscle tension. Results indicate that users show more signs of physiological stress when the vehicle drives autonomously than when the users is in control. Results also indicate that users show an additional increase in stress when the user reports low trust in the autonomous vehicle. These findings suggest that health-care professionals and manufactures should be aware of additional stress associated with self-driving technology.