Errant vehicles occur as a result of the driver losing control of the vehicle. This may be due to sudden illness, dozing off or skidding while attempting a manoeuvre. In containing such an errant vehicle on a highway, the priority is to avoid collision with other vehicles. A sloped highway median provides a run-off area for such vehicles where the vehicle can be slowed down and stopped without the danger of being re-directed into the path of other vehicles as may occur with edge barriers. Here, the effect of a containment barrier at the bottom of the sloped median is studied with a view to prevent the vehicle from being redirected outside the median after colliding with the barrier. The focus of this work is on the change of kinematic states due to the collision, so a momentum-based vehicle collision analysis is developed, with the collision energy loss related to the vehicle stiffness being considered by coefficient of restitution. The average maximum lateral displacements post-collision are read from the diagram of vehicle x-y trajectories. In this way, the most suitable median slope 1:6 is selected.