This paper presents an experimental study into the fundamental response of reinforced concrete members, which incorporate rubber particles obtained from recycled tyres, subjected to combined axial-bending loading conditions. Tests on confined circular members with and without internal hoops or external fibre-reinforced polymer (FRP) sheets are described. The results show that the rubber particles enhance the confinement level activated, with confined/unconfined strength and deformation capacity ratios at least twice those of conventional concrete members. The hoop-confined members provided with 30% rubber developed a typical reinforced concrete behaviour, with relatively limited deformation capacity in comparison with FRP-confined members. The external confinement substantially enhanced the ultimate rotation of members incorporating 30% rubber, with ductility factors reaching up to ten for relatively small eccentricity levels. An increase in rubber content to 60% had a detrimental effect on the axial capacity, but increased the ultimate rotation up to twice in comparison with members with 30% rubber. Based on the test results, a design-oriented constitutive model for FRP-confined concrete and a variable confinement procedure for assessing the strength interaction of circular sections are proposed. The suggested procedures capture, in a realistic manner, the influence of rubber content on the strength and deformation characteristics of confined members.