A novel and simple numerical model is introduced to describe the bond behavior of Carbon Fiber Reinforced Polymer (CFRP)-strengthened masonry specimens under direct shear tests. The model assumes that all nonlinearities are lumped at the interface between the reinforcement and the substrate. Both the CFRP and the support are reproduced by 4-noded elastic elements. The interface is meshed using a system of in-parallel trusses, namely cutoff bars (CoBs). A CoB is the simplest nonlinear finite element available in any commercial software, characterized by an elastic perfectly fragile or elastic perfectly plastic behavior. Assuming the typical tangential stress-slip relationship at the interface governed by an elastic phase followed by a linear descending branch, two elastic perfectly brittle CoBs in parallel are employed to reproduce the debonding failure of the reinforcement from the support. Such a discretization is connected to the plates by means of rigid beams. The reliability of the numerical model is validated through comparison with a set of experimental data related to masonry specimens reinforced with CFRP, available in the literature.