Seismic assessments of historical masonry buildings are affected by several sources of epistemic uncertainty. These are mainly the material and the modelling parameters and the displacement capacity of the elements. Additional sources of uncertainty lie in the non-linear connections, such as wall-to-wall and floor-to-wall connections. Latin Hypercube Sampling was performed to create 400 sets of 11 material and modelling parameters. The proposed approach is applied to historical stone masonry buildings with timber floors, which are modelled by an equivalent frame approach using a newly developed macroelement accounting for both in-plane and out-of-plane failure. Each building is modelled first with out-of-plane behaviour enabled and non-linear connections, and then with out-of-plane behaviour disabled and rigid connections. For each model and set of parameters, incremental dynamic analyses are performed until building failure and seismic fragility curves derived. The key material and modelling parameters influencing the performance of the buildings are determined based on the peak ground acceleration at failure, type of failure and failure location. This study finds that the predicted PGA at failure and the failure mode and location is as sensitive to the properties of the non-linear connections as to the material and displacement capacity parameters, indicating that analyses must account for this uncertainty to accurately assess the in-plane and out-of-plane failure modes of historical masonry buildings. It also shows that modelling the out-of-plane behaviour produces a significant impact on the seismic fragility curves.