Flash flooding is characterised by a rapid flooding phenomenon caused by intense rainfall. Despite being an extreme event with high uncertainty, the rainfall-run-off process is often regarded as deterministic (rather than stochastic). In this paper, the Soil Conservation Service (SCS) flood hydrograph uncertainty is quantified based on the Total Error Framework (TEF), and introduced into the model by applying perturbation in the input data and model parameters. The random perturbation component is stochastically modelled. A sensitivity analysis was carried out on the stochastic model parameters, using a real case study in the Azores (Portugal). The results showed that the flood hydrograph uncertainty varies over time, with its largest deviations occurring at the beginning of the flooding because of the uncertainty associated with the SCS method curve number parameter (correlation coefficient R2 of 0.86). Rainfall uncertainty was responsible for the uncertainty in the hydrograph peaks' magnitude (R2 = 0.93) while uncertainty in the propagation velocity was responsible for the uncertainty in the peaks' time (R2 = 0.97).