In this paper, we present and discuss the initial results of a large-scale research project involving laboratory and field investigations of abrasion resistance of different types of concrete. The decision to study in more detail the abrasion resistance of fibre-reinforced concrete with granulated rubber was based on the results of previous research projects, as well as on observations on the behaviour of concretes placed in the spillways of hydro power plants loaded with water and water-borne particles. Gravel aggregate, steel, polypropylene fibres, and granulated rubber were used to prepare the concrete. In the fibre-reinforced concretes without granulated rubber, the binding component consisted of cement and silica fume, but when granulated rubber was added, the binding component consisted of cement and a dry proportion of SBR latex. The results obtained by now, at an age of 90 days show that fibre-reinforced concretes with granulated rubber have an improved resistance to underwater abrasion, compared to fibre-reinforced concretes without granulated rubber.