This paper gives additional information on the use of new class of composites constituted by Basalt Fiber Reinforced Polymer (BFRP) bonded with epoxy resin to concrete specimens as an alternative confinement material for compressed concrete members with respect to carbon or glass fibers. From the experimental point of view, concrete cylinders are wrapped with continuous fibers, in the form of sheets, applying both full and partial discrete wrapping with BFRP straps, and then tested in compression. For comparison, few other concrete cylinders are wrapped with Carbon Fiber Reinforced Polymer (CFRP) sheets and tested in compression. The number and type of plies (full or partial wrapping), the type of loading (monotonic and cyclic actions) and the type of fiber (basalt and carbon) are the main variables investigated. The experimental results obtained from the compressive tests in terms of both stress–strain curves and failure modes show the possibility of reducing the brittleness of unconfined concrete, resulting significantly increased both the post-peak resistance and the axial strain of confined concrete corresponding to BFRP failure. Form the analytical standpoint, a review of the available models given in the literature is made and verified against the experimental data. Finally, a proposal for analytical expressions aimed at the calculation of the compressive strength and corresponding strain of confined concrete is provided also including the strain at BFRP failure.