This study presents an experimental assessment into the monotonic and cyclic compressive stress-strain rate-dependent response of rubberised one-part alkali-activated concrete. Three different volumetric crumb rubber replacement ratios of total natural aggregates (0%, 30% and 60%), and three different strain rates accounting for quasi-static, moderate seismic and severe seismic conditions are considered. The results indicate a reduction in the elastic modulus, compressive strength, and crushing energy in proportion to the rubber content regardless of the strain rate or loading condition, monotonic or cyclic. A reduction in the axial crushing strain is also obtained with the increase in rubber content within the ranges considered. The increase in strain rate leads to a proportional enhancement in elastic modulus, compressive strength, and axial crushing strain. Under cyclic conditions, the unloading and reloading branches of the stress-strain response fall within the monotonic curves. The cumulative energy dissipation from each first cyclic loop reduces with the increase in rubber content, whilst an increase in the loading rate results in a proportional increase in the cumulative energy dissipation. The unloading modulus is shown to be sensitive to the unloading strain, rubber content and strain rate, while the plastic residual strain is mainly influenced by the unloading strain. Analytical expressions to predict the reduction in elastic modulus, compressive strength, axial crushing strain, unloading modulus and plastic residual strain, with varying rubber contents and for the different strain rates considered, are proposed. Constitutive models representing the monotonic stress-strain response of rubberised alkali-activated concrete materials, as well as the unloading and reloading branches of the cyclic stress-strain response, are also given. Finally, formulations for the strain rate-dependent dynamic increase factors for the elastic modulus, compressive strength, and axial crushing strain are also provided.