Abstract Neutron-moderator scattering interactions in the thermal energy range are often treated with specialised cross section data derived from the Thermal Scattering Law S(α,β). This scattering law is calculated based on theoretical and experimental models that describe the structure and dynamics of the principle moderator molecule. In this work, a perturbation scheme based on the Total Monte Carlo method is described and the uncertainties of the parameters used to calculate S(α,β) for H in H2O and D and O in D2O from the ENDF/B-VIII.0 library were estimated and propagated through to the cross sections and to an integral criticality scenario in the OPAL Reactor, Sydney Australia, using the transport code Serpent. The calculated uncertainties in the total cross sections are in reasonable agreement with experimental data and provide a basis for future model refinement; uncertainties in several parameters used in the LEAPR of NJOY were identified as critical to specific energy regions and behaviours of the total cross sections. The effect on criticality of these uncertainties was found to be 48 pcm and 41 pcm for H2O and D2O, respectively, within the OPAL Reactor during a low-power configuration.