As the population living in cities is constantly growing, underground constructions represent a sustainable option for energy, goods, and people transportation in urban contexts. However, tunnelling produces surface settlements, whose magnitude depends on various factors related to soil properties, excavation process, and interaction phenomena with surface structures. These, in turn, can experience damage, whose severity is influenced by their relative position with respect to the tunnel, their structural features (type of construction and mechanical properties), and their geometry. These factors are also responsible for the said interaction, thus, in most cases, accurate settlements induced damage prediction and assessment require coupled analyses, which can be performed via numerical approaches such as finite elements. In this paper we present a numerical study in which tunnelling induced damage on masonry structures is assessed through three-dimensional coupled finite element models in which the nonlinear response of soil and structure are both accounted for. In particular, the anisotropic response of masonry is described through a constitutive model formulated in the framework of multilaminate plasticity. This entails the definition of pre-determined planes (head and bed joints) on which failure can occur while strength properties are affected by masonry internal structure. Damage is quantified by specific output variables, carrying information on plastic failure type, orientation, location, and severity, measured through strain magnitude. The study aims to investigate the influence of building stiffness and irregularity on the resulting damage, under consistent boundary conditions (tunnel, soil, and footing-soil interface properties).