This paper presents an experimental and numerical study into the behaviour of rubberised concrete-filled steel tubes (RuCFST), incorporating concrete with relatively high rubber replacements of up to 60% of mineral aggregates by volume. Axial compression, eccentric compression, and three-point bending tests on circular specimens are carried out and the results are used to validate the nonlinear procedures adopted in continuum finite element (FE) models of RuCFST members. A constitutive material model specific for confined rubberised concrete and associated modelling techniques, developed from existing procedures for concrete-filled steel tubes (CFST), is proposed for RuCFST members. The modelling techniques involve different damage definitions including low strength concrete with high rubber replacements in compression and bending. It is shown that the proposed modelling procedures can predict reliably the structural behaviour of circular RuCFST members under combined axial-bending conditions. The numerical procedures are then employed in undertaking a detailed parametric assessment for RuCFST cross-sections. The results are used to appraise current design procedures and to propose modifications that provide improved capacity predictions for a wide range of properties and loading conditions.