There is growing interest in the potential value of using phone applications that can monitor driver behaviour (Smartphone Driver Support Systems, 'SDSSs') in mitigating risky driving by young people. However, their value in this regard will only be realised if young people are willing to use this technology. This paper reports the findings of a study in which a novel structural model of willingness to use SDSSs was tested. Grounded in the driver monitoring and Technology Acceptance (TA) research literature, the model incorporates the perceived risks and gains associated with potential SDSS usage and additional social cognitive factors, including perceived usability and social influences. A total of 333 smartphone users, aged 18-24, with full Irish driving licenses completed an online questionnaire examining willingness or Behavioural Intention (BI) to uptake a SDSS. Following exploratory and confirmatory factor analyses, structural equation modelling indicated that perceived gains and social influence factors had significant direct effects on BI. Perceived risks and social influence also had significant indirect effects on BI, as mediated by perceived gains. Overall, this model accounted for 72.5% of the variance in willingness to uptake SDSSs. Multi-group structural models highlighted invariance of effects across gender, high and low risk drivers, and those likely or unlikely to adopt novel phone app technologies. These findings have implications for our understanding of the willingness of young drivers to adopt and use SDSSs, and highlight potential factors that could be targeted in behavioural change interventions seeking to improve usage rates.