Heritage masonry structures are often modelled as dry-jointed structures. On the one hand, it may correspond to the reality where the initial mortar was weak, missing, or has disappeared through time because of erosion and lixiviation. On the other hand, this modelling approach reduces complexity to the studied problem, both from an experimental and theoretical/numerical point of views, while being conservative. Still, for modelling purposes, in addition to the joint friction, numerical approaches require a specific elastic parameter, the dry-joint stiffness, which is often hard to estimate experimentally. This work numerically investigates the effect of the joint stiffness on the collapse of scaled-down tilting test experiments carried out on perforated dry-joint masonry shear walls. It is found that geometrical imperfections of bricks and the absence of vertical precompression load can lead to very low equivalent dry-joint stiffness, which strongly affects the results, both in terms of collapse and damage limit state (DLS) loads, with practical implications for the engineering practice.