This paper presents experimental and numerical assessments into the compressive stress-strain behaviour of circular FRP-confined rubberised alkali-activated concrete with unidirectional sheets incorporating fibres in the hoop direction. The parameters investigated in the experimental programme include three different rubber contents of 0%, 30% and 60% volumetric replacement of the total natural aggregates and three confinement levels of 1–3 aramid FRP layers. The numerical assessment is performed in ABAQUS/CAE and a new strain hardening-softening function is developed for the compressive behaviour in the Concrete Damaged Plasticity material model, which captures the passive confinement imparted by the FRP jacket on the rubberised concrete. The numerical results are validated against the experimental results and a parametric study involving 240 models covering a wide range of parameters, including varying FRP materials (basalt, glass, aramid, and carbon), reference concrete grades, rubber replacement ratios, and confinement levels, is performed. The experimental results show an increase in the confinement effectiveness, i.e., confined-to-unconfined strength, by 66.7% and 103.4% for specimens with 0% and 60% crumb rubber replacement ratio, respectively, as the number of FRP layers increase from 1 to 3. Test specimens with 0% and 60% crumb rubber replacement ratio indicate an increase in the ultimate axial strain by 228.2% and 76.2%, respectively, as the number of FRP layers increase from 1 to 3. The observed hoop rupture strain reduces by 32.8% and 21.3% for specimens with 0% and 60% crumb rubber replacement ratio as the number of FRP layers increase from 1 to 3, showing a trend of reduction in the hoop rupture strain with higher FRP confinement layers and rubber content. The numerical results show that the enhancement in compressive strength is linearly proportional to the confinement ratio and is only marginally influenced by the FRP jacket stiffness at a given confinement ratio. The ultimate axial strain enhancement is also linearly proportional to the confinement ratio but is dependent on the FRP jacket stiffness. The compressive stress-strain curve for sufficiently confined specimens is also shown to be well represented by a bi-linear curve with hardening. Based on the findings, a design-oriented model is introduced for sufficiently confined specimens and is shown to be in close agreement with the experimental results.