In this study, the propagation of uncertainties of loading and structural parameters on the thunderstorm gust response factor is studied for the case of a slender vertical structure within a non-probabilistic framework through improved interval analysis. Specifically, starting from the thunderstorm data available together with a model for the vertical profile of the mean velocity from the literature, suitable bounds of the relevant loading parameters are defined. Then, based on a closed-form solution for the gust factor proposed by the first two authors and characterising also the structural parameters as interval variables, the interval analysis is applied to obtain the bounds of the thunderstorm gust response factor. Results show that, for the structural case considered, the uncertainties on the thunderstorm parameters have a greater impact on the thunderstorm gust response factor with respect to the uncertainties on the structural parameters.