Autonomous driving systems (ADSs) must be sufficiently tested to ensure their safety. Though various ADS testing methods have shown promising results, they are limited to a fixed vehicle characteristics setting (VCS). The impact of variations in vehicle characteristics (e.g., mass, tire friction) on the safety of ADSs has not been sufficiently and systematically studied. Such variations are often due to wear and tear, production errors and so on, which may lead to unexpected driving behaviours of ADSs. To this end, in this article, we propose a method, named SafeVar , to systematically find minimum variations to the original vehicle characteristics setting, which affect the safety of the ADS deployed on the vehicle. To evaluate the effectiveness of SafeVar , we employed two ADSs and conducted experiments with two driving scenarios. Results show that SafeVar , equipped with NSGA-II, generates more critical settings that put the vehicle into unsafe situations, as compared with the baseline algorithm. We also identified critical vehicle characteristics and reported to which extent varying their settings put the ADS vehicle into unsafe situations.