This paper presents an experimental study into the fundamental response of reinforced concrete members, incorporating 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 FRP sheets are described. The results show that the rubber particles enhance the confinement level activated, with confined-to-unconfined strength and deformation capacity ratios at least two folds 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 to FRP-confined members. The external confinement enhanced substantially 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 two folds in comparison to 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.