Fiber (or fabric) reinforced cementitious matrix (FRCM) composites represent an attractive alternative to fiber reinforced polymer (FRP) composites as externally bonded reinforcement (EBR) of existing reinforced concrete (RC) and masonry structural members. Although FRCM composites generally provide lower mechanical properties than FRP composites, they are permeable to vapor, can be removed with limited damage of the substrate, and have good resistance to relatively high temperatures. FRCM composites have been increasingly adopted to strengthen existing masonry members, such as walls, vaults, and domes. Due to the large surface of these members, different pieces of fiber textile (fabric) need to be overlapped (i.e. lap-spliced) to guarantee the stress-transfer between composite and substrate for the entire strengthened surface (excluding the anchorage length). Therefore, the lap-splice length represents a fundamental parameter for the effectiveness of the externally bonded reinforcement. However, limited work was carried out to investigate the stress-transfer mechanism between lap-spliced fiber layers.