In recent years giant progress has been made in the understanding of structural behaviour and the development of proficient intervention strategies on existing masonry structures. The retrofit using compatible and efficient structural strengthening techniques was investigated primarily considering new technologies based on Fiber Reinforced Polymers (FRP), i.e. fibres with an organic resin matrix. Lot of knowledge was developed, mainly based on the assumption of linear elasticity for FRP. However nowadays resin matrix has been substituted by inorganic mortar matrices, yielding to the family of Fiber Reinforced Cementitious Matrix (FRCM) systems. Mortar matrix is more compatible with masonry, however FRCM does not behave like as FRP because the matrix cracks before fibre rupture and the contribution of matrix (in terms of stiffness in particular) is not negligible as it is for the resin, hence linear behaviour is substituted by a bi- or even tri-linear behaviour. The easiest way was to extend the models for FRP to FRCM, however it has never been clarified the impact of peculiar behaviour of FRCM on the analyses conducted assuming FRP, i.e. fiber only, behaviour and no compressive strength. The main aim of this study is to develop a general model for flexural behaviour of FRCM strengthened masonry based on dimensionless analysis. In fact, being independent on the geometrical and mechanical parameters of the masonry and of the strengthening system, the results represent the basis for the development of standardized design and / or verification methodologies. In particular it is remarked the impact of different local behaviours of FRCM (and FRP for comparison purposes) materials on the global flexural response of strengthened masonry.