Every year, many pedestrians and cyclists die in road crashes, most commonly when they cross a car's travel path. To avoid these crashes, car companies have already developed safety systems that control the car or warn the driver (such as autonomous emergency braking and frontal collision warning systems, respectively). However, these systems need to be improved; they are still not perfect. We can improve these systems by predicting drivers' control using mathematical models. Unfortunately, only a limited number of models are currently available, and few deal with crossing situations. This thesis supports the design and evaluation of safety systems that can predict driver control, through multiple objectives: 1) study driver behaviour when a cyclist or a pedestrian crosses the travel path, 2) create models that can predict driver control, 3) update evaluation programmes (for instance, Euro NCAP) with new knowledge to guide the development of their test protocols, and 4) develop a way to evaluate the potential impact of safety systems using virtual simulations. Results of our experiments show that the moment in which a cyclist or a pedestrian becomes visible to the driver (appearance time) had the largest effect on the driver’s braking. The data, recorded during driver behaviour experiments in driving simulators and on a test track, were used to devise four different predictive mathematical models: a gas-pedal release and braking initiation model in crossing-pedestrian scenarios, and a braking initiation model, a discomfort model, and a brake-pedal position model for crossing-cyclist scenarios. The brake-pedal position model is the most advanced model developed in this thesis. These models can provide information about the driver that can be used to determine the ideal activation time for a safety system in order to maximise its acceptance by the driver. The models can also be used in computer simulations to evaluate the systems' safety benefits. In fact, the thesis work demonstrated that models are an important part of the computer simulations used to evaluate systems' safety benefits. Not only has this thesis acquired more knowledge about driver behaviour, but it also delivers this knowledge in the form of models that can be used to improve the safety systems and test protocols of assessment programmes.