The contact of a rubber track or a tyre tread with an edge corner is a process involved in many practical applications, i.e. traversing rough terrain and stair climbing. This paper presents a rigorous analysis along with experimental results to study what happens during the contact between a running gear and an edge corner as well as what forces are exchanged between these two elements by providing also a comparison between existing theoretical methods to assess which one is the most accurate. A testbed has been specifically developed for this research work to analyse the behaviour of a rubber specimen in contact with a step-like obstacle. The experimental results highlighted that the forces exchanged between a belt and a corner edge depend only on the relative inclination between the two sides of the belt and on the coefficient of friction while a pneumatic tyre patch behaves similarly to a belt when it is in contact with a step corner edge.