The paper presents the results of the evaluation of the seismic safety of the Ancien Hôpital de Sion, an important Swiss architectural heritage building, sited in the Canton of Valais, the region with the highest seismic hazard in Switzerland. Three-dimensional Applied Element (AEM) modelling of the whole structure has been performed and validated. The adopted modelling strategy, together with non-linear dynamic analysis, was able to represent the actual behaviour and failure mechanisms typical of complex masonry structures, in addition to a good computational efficiency compared to other available numerical approaches. The local collapse mechanisms have been also studied through a kinematic limit analysis based on rigid block rotation. Both linear and non-linear approaches have been followed together with the capacity spectrum method. The results provided by the different methodologies have been compared with the aim to provide possible insights concerning a general procedure for the assessment of the safety of such type of structures.