Susceptibility to structural damage can be characterized by a fragility curve, which is expressed as a normal or lognormal cumulative distribution of the conditional probabilities of reaching or exceeding a particular damage state, for given values of the demand parameter. Such curves have been produced for a variety of damage states in different categories of buildings exposed to tsunami loading in different parts of the world, with the demand parameter taken as inundation depth. Harmonization was sought across these studies with respect to the median inundation depth. Three categories of single-storey buildings were identified based on construction material, namely reinforced concrete, masonry and timber. The median inundation depths for the complete damage state decreased from reinforced concrete (5.4–7.3 m) through masonry (2.3–2.5 m) to timber (~1.6 m) structures. The fairly narrow ranges above represent a number of different studies and indicate that a common family of curves or “bands” can be arrived at. Such ranges were identified for other partial damage states too. Our genuinely original contribution is a probabilistic model that was developed using a Monte Carlo simulation to produce synthetic fragility functions for masonry and reinforced concrete structures under tsunami loading. The probabilistic model consisted of a geometric model that captured the geometrical and wall-type variations of the building lot, a loading function and a set of failure criteria, all of which required appropriate simplifying assumptions. The resulting synthetic fragility curves matched the fragility curves based on observed tsunami damage for the complete collapse damage state reasonably well.