Abstract Historical masonry buildings, composed of adobe/brick building blocks that are connected together with clay, lime-clay, or gypsum-clay mortars are vulnerable to earthquake. Many of these historical buildings are world heritage listed. They are highly valued and it is important that they are evaluated for their capacity to resist earthquakes, or strengthened if found not to be adequate. In this paper, the structural behavior and lateral resistance of a heritage brick vault with adobe piers built in 1935, Yazd, Iran is investigated under lateral loads. A nonlinear finite element analysis is used based on the concepts of homogenized material and smeared model in which the masonry is modelled as an anisotropic continuum. For this macro-modelling, the mechanical properties of continuum masonry are determined by experimental tests. Based on the literature review performed in this paper, no similar tests on structures of this kind have been identified elsewhere. Finally, the vault and the piers were retrofitted using Carbon Fiber Reinforced Polymer (CFRP) laminates at extrados in order to compare their failure mechanisms and lateral strength before and after retrofitting.