In the management of water resources, it is necessary to balance the demands of multiple uses of water and water availability, while enabling use in an environmentally sustainable way. Probability distributions of flow rates are essential tools for assessing water availability. The objectives of this work were to analyze the best probability distribution that conforms to the annual minimum daily average discharge for periods of seven consecutive days (Q7) for 14 stream gauging stations in the Das Velhas River Basin and to identify possible trends in Q7 time series and in bi monthly and annual sets of daily discharges in three key stream gauging stations. The quality of fit was verified by the Anderson-Darling test (A-D). The selection of the models that presented the best fit was done according to the Bayesian Information Criterion (BIC). The Mann-Kendall test was used to verify trends in time series of discharge. In general, better measures of quality of fit were obtained for the probability distributions Gumbel and Rayleigh. Negative trends in discharge distributions were verified in the three stations. For the Várzea da Palma station, the closest to the river mouth, negative and significant trends were found for the Q7 data and daily average discharge for every bimester except the first.