Fluid jets are increasingly used to process and machine tension-softening materials. Typical applications are drilling, cutting, fragmentation, hydrodemolition and 3D-machining. Tension-softening materials, such as concrete, reinforced ceramics, most rocks and solidified impurities, are quasi-brittle behaving materials characterised by a so-called fracture process zone. Therefore, linear elastic fracture mechanics does not suitably cover these materials. It is also known that conventional strength parameters, such as compressive strength, cannot describe the resistance of this group of materials against fluid jet erosion. In this paper, the behaviour of cement paste, mortar and concrete during the erosion by high-speed waterjets with velocities up to 470 m s−1 is investigated. The results of SEM-studies are presented that clearly illuminates features of quasi-brittle behaviour, including grain bridging, microcracking and crack branching. It is also found that the erosion process is strongly determined by the size of the aggregate (inclusions) in the material. It is concluded that a non-linear fracture resistance parameter may be suitable to estimate the erosion resistance of the material. It is found that the brittleness BM – the inverse of the characteristic length of a material – is a suitable resistance parameter. A very good relationship between the brittleness and the volumetric erosion rate estimated from 24 different types of concrete could be obtained.