A stochastic model, based on the recent developments in the theory of extreme values, is presented to describe and analyze excessive streamflows. The model is a particular stochastic process x^(t) defined as the maximum term among a random number of random observations in an interval of time [0, t]. Since the number of hydrograph peaks in [0, t] that exceed a certain level x₀ and the magnitudes of these peaks are random variables, the foregoing model seems to conform well to the flood phenomenon. The passage time T(x) of the process x^(t) relevant to the risk evaluation in the design of hydraulic structures is also considered. The results obtained are applied on the 72‐year record of the Susquehanna River at Wilkes‐Barre, Pennsylvania. Theoretical and observed results agree reasonably well.