Uncertain parameters in the transient analysis of pipe networks lead to uncertain responses. Typical uncertainties are nodal demand, pipe friction coefficient and wave speed, which not only are imprecise in nature but also change significantly over time. Exploiting the fuzzy set theory and a simple scheme of the simulated annealing method, a conceptual model is developed. It can take into account the uncertainties of conventional transient analysis. This model helps designers of pipe systems in finding out the extent to which uncertainties in the inputs can spread to the transient highest and lowest pressures. A real piping system is analyzed herein as the case study. The results show that the transient extreme pressures can be highly affected by the uncertainties.