This paper deals with the experimental behaviour of rubberised concrete members subjected to asymmetric four-point shear loading. A detailed account of tests on 15 prismatic members using conventional concrete as well as rubberised concrete, with relatively high replacement ratios of both fine and coarse mineral aggregates with rubber particles, is given. The results enable direct assessment of strength and complete deformation characteristics including the post-peak response for ultimate behaviour governed both by shear and mixed-mode tensile-shear. After describing the material properties, mix designs and member details, the main observations from detailed measurements of the crack kinematics through a digital image correlation monitoring system, with focus on members developing shear-governed response, are reported. Complementary numerical studies are undertaken using nonlinear finite element procedures which are validated against tests developing shear-governed failures. In order to provide further insight into the key response characteristics, particularly those related to ultimate strength, a number of numerical sensitivity studies employing various constitutive parameters are also carried out. Moreover, comparative assessments in terms of shear resistance, toughness and force transfer across the cracked interfaces are performed and discussed. The detailed test measurements, coupled with the results obtained from the numerical simulations, permit the definition of expressions for representing the shear resistance as a function of the rubber content and concrete compressive strength.