This study examines the lateral cyclic response of square steel tubes infilled with rubberised alkali-activated concrete through experimental investigations and complementary numerical assessments. The tests include steel members infilled with concrete incorporating up to 60% volumetric crumb rubber replacement of total natural aggregates and subjected to co-existing axial load levels of up to 20% of the cross-section axial capacity. Detailed numerical simulations are also carried out to provide further insights into the behaviour of the test specimens as well as to validate representative pushover procedures which are used for subsequent parametric evaluations. Key material, geometric and loading parameters are considered, including the rubber content, concrete infill strength, steel yield strength, tube cross-section slenderness, and applied axial load ratio. The experimental results, including those from detailed digital image correlation measurements, are used alongside those from numerical simulations, to assess salient response parameters related to the stiffness, capacity, and ductility of the composite members. It is shown that, despite the relatively low levels of confinement typically mobilised in rectangular tubes, the increase in rubber content can offer an enhancement in inelastic parameters such as the plastic hinge length and deformation ductility, depending on the specific cross-section properties. The results also indicate that alkali-activated concrete materials can be effectively used in infilled tubes, provided that the observed lower stiffness, when compared to conventional concrete, is accounted for in design. Finally, the adequacy of typical analytical expressions, used in codified guidance for evaluating the stiffness and capacity, is examined, and adjustments are proposed where necessary in support of practical design procedures.