With its internal axes of 37.23 by 24.89 m, the dome of the Sanctuary of Vicoforte, Italy, is the fifth biggest in the world in absolute term, and by far the largest elliptical dome ever built. The dome-drum system has suffered since the beginning from significant structural problems, partly due to soil settlements and arising from its bold structural configuration. This paper deals with the modelling strategies adopted in the assessment of the structural reliability of the monument, a project undertaken in recent years following the strengthening intervention operated in 1985 with the application of active tie-bars around the perimeter at the top of the drum. The structural behaviour of the construction was modelled according to two different approaches: limit analysis and finite element analysis (linear and non-linear). This paper presents the results obtained by non-linear constitutive models for the masonry.