Masonry structures present a high portion of the world's building cultural heritage. Most of these masonry structures are exposed to cyclic static and dynamic loads (wind, earthquakes, soil expansion,...) which can progressively damage the structure and lead to structural failure. Thus, predicting the mechanical response of such structures under such a loading case is mandatory to preserve them. \par When dealing with a cyclic loading, modelling accurately the damage and plastic behaviour of the masonry constituents and more specifically the block/mortar interface is necessary to capture the structure's response. A recent study highlights the damage-plastic behaviour of block/mortar interface and shows that in the post-peak regime residual displacements increase strongly. To take into account this non-linear phenomenon, different interface models based on damage and classical plasticity theories were developed, in both discrete element and finite element formalism. In this work, plasticity is incorporated in an existing frictional cohesive zone model using an ad-hoc approach by considering that the dissipated plastic energy (generating residual displacements) is coupled to the dissipated cohesive energy (generating damage)through a proportional relationship between the two energies. Thus, the residual displacement is computed based on the damage value. The developed model is advantageous since plasticity was taken into account through simple modifications of an existing frictional cohesive zone model that was already been validated on masonry structures under monotonic loading. The proposed model is validated by comparing the numerical and experimental results of a masonry wall subjected to a compression and a cyclic shear loading.