Masonry is a composite anisotropic material characterised by a quasi-brittle response. A realistic representation of various complex local phenomena, such as brick sliding and separation, is needed to accurately model masonry structures, especially when subjected to extreme actions, like blast loads generated from malicious or accidental explosions. Since mortar layers and brick-mortar interfaces act as weak planes where cracks initiate and propagate, they control the ultimate response of unreinforced masonry (URM). For these reasons, a detailed mesoscale modelling approach that considers the characteristics of the brick-mortar interfaces is used in this study to investigate the response of URM walls under blast loads. The influence of various interface parameters, brick-unit characteristics, blast-load intensity, and boundary conditions is examined through parametric and sensitivity analyses. It was found that friction between brick units is the most critical characteristic for accurately modelling the interface between units. The outputs of this study will help better understand the behaviour of URM structures under blast loads, leading to improved design of appropriate protective measures.