Debris and hyper-concentrated flows are among the most destructive of all water-related disasters. They mainly affect mountain areas in a wide range of morphoclimatic environments and in recent years have attracted more and more attention from the scientific and professional communities and concern from public awareness, due to the increasing frequency with which they occur and the death toll they claim. In this context, achieving a set of debris and hyper-concentrated flow constitutive equations is a task that has been given particular attention by scientists during the second half of the last century.In relation to these issues, this paper reviews the most updated and effective geotechnical and fluid-dynamic procedures nowadays available, suitable to predict the triggering and mobilising processes of these phenomena, and proposes a mathematical model that is able to assess the depth of the wave and the velocities of the liquid and solid phases of both non-stratified (mature) and stratified (immature) flows following flash-floods and dam-break events in one and two dimensional cases.Different experimental cases of dam-break situations in a square section channel were considered for the purpose of comparing results.These tools will allow, on one hand, to better focus on what to observe in the field and, on the other hand, to improve both mitigation measures and hazard mapping procedures. Keywords: debris flow, rheological behaviour of the mixture, slope failure, numerical models, laboratory and field tests.