This paper presents the results of the investigation on the seismic behaviour of an important historical masonry building, the "Ancien Hôpital de Sion". The building is sited in the city of Sion, capital of the Canton of Valais, characterized by the highest seismic hazard in Switzerland. The complexity of the structure poses challenging questions in the evaluation of its behaviour, requiring the use of different assessment techniques. A detailed three-dimensional model of the building was developed through the applied element method (AEM), accounting for all possible failure mechanisms occurring in a masonry structure. The analysis of damage distributions allowed to identify the most vulnerable areas of the building and to obtain indications on the necessity of seismic strengthening. The effects of the level of connection offered by the timber floors was also investigated. The kinematic limit analysis was employed for the evaluation of the building's capacity through possible overturning of the most vulnerable portions of masonry. The collapse mechanisms analysis was performed with both linear and non-linear approaches applying the capacity spectrum method. The numerical and the analytical results were finally compared in order to evidence the applicability of the procedure for the assessment of historical buildings.