This paper shows a numerical investigation with single-lap shear bond tests between Peruvian brick masonry and SRG system. For this purpose, the finite element method, elements and constitutive models implemented in ABAQUS library were used. Eight-node continuum elements were employed for modelling mortar, masonry and steel fibers assuming a linear-elastic behaviour for the last two materials. Eight-node cohesive elements with zero-thickness were used to model substrate-mortar and steel-mortar interfaces. Due to experimental results showed the detachment of the steel fiber from the mortar accompanied by cracking of the outer mortar layer, the non-linearity of the mortar was also considered by using a Concrete Damage Plasticity constitutive model. The effect of the mortar non-linearity was compared with other models assuming a linear and rigid material for mortar, as recommended by literature. This shows that modelling a non-linear mortar leads to more accurate results for future design and strengthening purposes, thus, its implementation is encouraged. A comparison in time between Bond–Slip Law (BSL) at steel–mortar interface and mortar constitutive law is analysed in order to investigate the stress-transfer mechanism during single–lap shear tests.