Application of fiber reinforced polymers (FRPs) for externally bonded reinforcement (EBR) of masonry structures has received extensive attention during the past two decades. However, FRPs are found to be hardly compatible with some structures, especially for historical masonry which exhibiting poor durability and long-term performance. As an alternative, the use of innovative composite materials based on continuous fibers embedded in inorganic matrices (Fabric Reinforced Cementitious Matrix (FRCM)) has found recent attention. The typical experimental stress–strain behavior exhibited by a FRCM composite under a monotonic direct tensile test is a tri-linear curve with a first phase that increases linearly according to mortar’s elastic modulus, a second phase which mortar undergoes a multi-cracking process, and a last phase which the mortar is fully cracked and the composite system behaves almost linearly stiffness of the fabric. This paper presents numerical simulation of the nonlinear tensile behavior of FRCM specimens. The modeling strategy was initially validated by simulating a monotonic direct tensile test. The adopted modeling strategy was then used to predict the FRCM specimens not only in monotonic but also cyclic tensile test. A final objective of the numerical simulation was to study and compare possible material used as fiber or grid in mortar based composites. At this aim, different material fibers were used for continuous fiber belonging to FRCM specimens.