Rubberised concrete has been suggested for structures subjected to dynamic loadings, such as impact and blast, however, the understanding of the dynamic behaviour with rubber replacement and the influence of the particle size is still limited. This paper investigates the impact behaviour of rubberised concrete using both experimental and numerical studies. Split Hopkinson Pressure Bar tests under higher strain rates up to 181 s−1 were used to analyse the experimental dynamic behaviour using concrete specimens with a low volume of coarse and fine aggregates replaced by tyre shreds (15 mm) and tyre crumbs (2–4 mm), respectively. Under the same impact, rubberised concrete specimens demonstrated ductile failures, high dynamic increase factors, and increased normalised toughness moduli. Furthermore, rubberised concrete with the larger tyre particles showed increased ductility and normalised toughness moduli than that with the smaller tyre particles. Conversely, the specimens with smaller tyre particles were revealed to have higher dynamic strengths and dynamic increase factors. The numerical model in LS-DYNA, using the Karagozian and Case material model, was calibrated to reflect the observed rubberised concrete experimental performance. The calibration technique was validated by accurately predicting the dynamic tyre particle size effect of rubberised concrete numerically. The results proved that low-level rubber replaced concrete can be potentially used in impact resistant structures as there is a good balance between quasi-static and increased dynamic impact resistance for more sustainable constructions.