AbstractIn an era marked by the urgent need to ensure the safety of existing buildings according to current standards, evaluating the stability of masonry structures against hazard events has become a significant challenge. Despite the versatility and durability of masonry, structural assessments are hampered by factors such as limited information on material properties, irregular geometries, and ageing. To address this issue, numerous modelling techniques have been developed, supported by extensive scientific literature. However, significant factors related to the case study replication, such as the geometric complexity, the mechanical behaviour of masonry, the loading applications, contribute to the challenges associated with modelling procedures, including computational time, discretization procedures, and step incrementation. This paper critically discusses the most innovative modelling approaches. Specifically, it aims to compare the efficiency of the Distinct Element (discontinuous) Methods and the Finite Element (continuous) Method, both applied to the numerical simulation of a case study structure severely damaged by the 2016 Central Italy earthquake under lateral loading conditions. The continuous method is analysed using Midas FEA NX©, while the discontinuous methods are studied using 3DEC© and LMGC90© software, each with different contact conditions. Finally, the investigation highlights the main advantages and disadvantages of each method. In particular, the discontinuous method demonstrates reliability in accurately replicating failure patterns, whereas the continuous method allows for a faster model setup, making it suitable for preliminary studies on structural dynamics.