Masonry columns often exhibit a lack of load-carrying capacity that is due to overloads and do not provide any ductility or dissipation capacity under seismic forces. Column confinement has been extensively studied as an effective technique, which could mitigate these structural vulnerabilities. The confinement of masonry columns will be studied in this paper, by considering fabric–reinforced cementitious matrix (FRCM) materials as external jackets. Due to the lack of information in the scientific literature, a new analysis-oriented model (AOM) for the prediction of the axial stress–strain law will be presented and discussed in this paper. The proposed AOM consists of a system of equations that make several assumptions: crossing the predicted peak point (strength and relative strain), crossing the ultimate point (80% residual strength and relative strain), and the horizontal tangent at the peak point and the initial (linear elastic) slope derived from the geometry and mechanical properties of the materials involved. The AOM was demonstrated to be simple and accurate, based on Pearson’s test (χ2); therefore, the proposed approach could be considered for future design equations. In addition, this paper will illustrate and discuss the validation of two available design-oriented models (DOMs), which could predict the axial strength of FRCM jacketed columns, by comparing the theoretical results with a database of experimental results that is available in the scientific literature. Novel formulas for the computation of both the peak and ultimate axial strains will be further proposed, as the basis for a design procedure. Their accuracy was demonstrated by considering an experimental versus theoretical comparison.