Our article investigates the response of the synthetic unit hydrographs (SUH) to parameter changes using sensitivity analysis. The beta and Weibull probability density functions and the objective function that includes both the peak discharge and time to peak were chosen to construct the SUHs for a small mountain catchment. The absolute and relative dependences between the distribution parameter changes and changes in the peak discharge and time to peak are measured using the sensitivity analysis methods which include both differential calculus and numerical computations. The Weibull SUH turned out to be more sensitive than the beta SUH when modeling the maximum discharge. The impacts of both parameters of the beta SUH and one parameter of the Weibull SUH on the time to peak are comparable, while the influence of the second parameter of the Weibull SUH is weaker. The results of validation showed good efficiency of the models and compatibility with Snyder’s model. They serve as an effective tool in assessing flood risk.