This paper describes the concentric compression test results of carbon fibre reinforced polymer (CFRP) composite sheet jacketed concrete specimens with circular, square and rectangular cross-sections. In the experimental program, pre-damaged specimens and repeated compressive loads were considered as well as undamaged specimens and monotonic compressive loads. The contribution of CFRP composite jackets to the compressive behaviour of the specimens is evaluated quantitatively, in terms of strength, longitudinal and lateral deformability and energy dissipation. Simple analytical expressions are proposed for compressive strength and ultimate axial strain that are valid for CFRP composite jacketed concrete with circular, square and rectangular cross-sections. The analytical results obtained by the proposed expressions are in good agreement with the experimental data obtained in this study, as well as the experimental data available in literature.