The calibration of computational models using Bayesian updating has recently gained ground in the structural engineering field [1]. In particular, Bayesian inference has emerged as a powerful statistical tool in the domain of historical constructions, where the imperative to preserve the values of these structures often imposes strict limits on the realization of destructive tests for characterizing mechanical properties of building materials. Simultaneously, including material uncertainties is essential to assess their effect on monitored output quantities while considering available data for model calibration through Bayesian methods. However, it requires performing several deterministic calls according to the chosen sampling technique. This can be impractical for demanding analyses if not for some surrogation technique that enables substituting resource-intensive FE models with analytical computations [2]. This paper addresses sensitivity analyses (SAs) on mechanical parameters of masonry in nonlinear FE modeling of a substructure of the Baptistery of Pisa (Italy) made of a dodecahedral dome, an arched drum, and supporting pillars, namely a potential past intermediate configuration of the centuries-old construction process. Particularly, uncertainties on the drum’s mechanical properties are considered for its crucial role in the stability of the structure. The work presents an original way of employing SAs to study the model response in terms of crack length at the dome’s edges, thus facilitating mutual understanding between the most likely values of the drum properties for crack development and potential past stages. A first evaluation allowed the problem dimension reduction by pinpointing parameters not influencing the monitored quantity. A subsequent SA based on Sobol’s indices computation was performed with probability distributions suitably modified to ensure the damage was coherent with real crack patterns and input parameters were calibrated through Bayesian inference. Uncertainty quantification (UQ) was carried out through gPCE-based analytical surface reconstruction. Then, the practical achievability of the updated drum’s mechanical properties values was evaluated. In this sense, UQ was crucial to assess the admissibility of the past stage represented by the analyzed substructure, which is essential for subsequent staged construction analyses on the whole construction to seek the causes of the current crack pattern. Finally, the calibration of