Inflatable flexible membrane dams (IFMD) have been used for the past 40 years in river and coastal engineering applications. Despite an increasing interest for IFMD, little information is available on the hydraulic performances of IFMD during overflow periods. Overflow situations may occur with deflated or inflated membranes. Both situations are described. It has been recognised that overflowing waters may induce some form of fluid-structure interactions, which might cause vibrations of the IFMD structure, leading to damage or destruction of the membrane. Several flow instability mechanisms are reviewed and the associated hazards are discussed. For overflow situations above inflated dams, new flow calculations are detailed and the results give new information on the wall pressure distribution along the downstream face of the dam. A mechanism of cavitating flow separation is also explained.