Hygrothermal models are important tools for assessing durability risks in building envelopes, such as biological growth (mould and wood rot fungi), corrosion and freeze-thaw action in masonry. Hygrothermal modelling of mass masonry wall assemblies are known to have numerous weaknesses and gaps in our understanding. First, there are significant uncertainties relating to model inputs including material properties and boundary conditions. Second, it is difficult to calibrate model results against data measured in the field. Third, two and threedimensional interactions between adjacent materials in masonry assemblies are poorly understood and are rarely modelled in practice. And fourth, geometric irregularities, imperfections and the effects of decay are rarely considered by modellers. Combined, these uncertainties can lead to reduced confidence in the model's conclusion and alter our opinions on the durability risks and whether retrofits such as interior insulation are appropriate or not. This doctoral thesis examines how uncertainty factors into hygrothermal modelling of heritage masonry, and how it can be reduced, and or, acknowledged in practice. This is demonstrated using a combination of simulation studies and on-site monitoring work. Three peer-reviewed papers which demonstrate examples of uncertainty in hygrothermal modelling are presented.The first paper presents a methodology for integrating calibrated hygrothermal and energy models of the Southwest Tower of the East Block for the purpose of assessing durability. This project consisted of in-situ monitoring of the masonry and ii interior climate of the Southwest Tower for over a year. The calibrated energy model was used as basis for estimating the net benefit of interior climate retrofits on the durability of the masonry. The calibrated hygrothermal model was not as successful, but the lessons learned were transferable to the third paper.The second paper examines the imperfect nature of the mortar-unit interface in masonry and how this affects moisture transfer into and out of the wall. Simulations showed that modelling this interface explicitly as a fracture will increase water absorption during wetting periods, but also help slightly with releasing moisture under drying conditions.The third paper examines the uncertainty in geometry and construction of the rubble core walls of the East Block. The wall's stack pattern is highly irregular and the core of the walls are known to have significant levels of voids which can act like insulating layers, or act as mini-rainscreens slowing moisture transfer into the wall. A Python script was developed to stochastically-generate sections of walls with and without voids. A significant variation in state variables, and heat and moisture fluxes was found between stochastically generated geometries in the mortar joints and in the rubble core. This variation increased with the number of voids.Overall, this research contributes to efforts make hygrothermal modelling of masonry more accurate and more intuitive for practiti...