Built cultural heritage anchors the cultural identities of peoples worldwide and constitutes capital for sustainable development. Maintenance and adequate conservation actions are often absent, increasing the exposure of historical structures to natural hazards such as earthquakes, floods, and the long-term effects of climate change. On August 24, 2016, a Mw 6.8 earthquake occurred in Chauk, Myanmar, with an epicentral distance of approximately 40 km away from the UNESCO archaeological site of Bagan. Despite past interventions to strengthen temples in the area, recurring critical damage such as overturning and shear-sliding were observed in situ. This study presents a numerical methodology for a vulnerability assessment on the site, using four temples as examples of different structural typologies. The methodology aims to capture and interpret the observed collapses in situ, as well as to validate a computationally feasible modelling strategy. The numerical models are based on elastic bodies and discontinuous interfaces, aiming to simulate rocking and sliding failure. The temples are large, so two simplifications reducing computational cost are proposed and examined: first, use of three single-degree-of-freedom (SDOF) oscillators as substitutes for the dynamic behaviour of the ground floor; and second, neglect of the local disintegration mechanisms of masonry. The temples were assessed against 11 ground motion records including the 2016 Chauk earthquake, a simulation of the same, and nine physics-based ground motion simulations for a rupture scenario of Mw 7.3. The results of the 44 analyses are given in terms of rocking angles and sliding displacements. Collapses and other serious vulnerabilities were found in most of the slender structures of the temples, including the central spires and the small corner stupas placed at different terrace levels.