This paper introduces an extension of the Global Gradient Algorithm (GGA) to directly solve unsteady flow problems arising from the presence of variable head water storage devices, such as tanks, in Extended Period Simulations (EPS) of looped water distribution networks (WDN). Such a modification of the original algorithm was motivated by the need to overcome oscillations and instabilities reported by several users of EPANET, a worldwide available package, which uses the GGA to solve the looped WDN equations. The set of partial differential equations describing the time and space behaviour of a water distribution system is here presented. It is shown how an unsteady flow GGA can be derived by simple modifications of the original steady-state GGA. The performances of the new algorithm, referred to as EPS-GGA, are compared with the results provided by EPANET on an extremely simplified example, the solution of which is qualitatively known. As opposed to EPANET which shows significant instabilities, the EPS-GGA is stable under a wide variety of increasing integration time intervals.