Two-dimensional gravity currents flowing down a slope have been investigated theoretically. The gravity currents are generated by a constant mass flux of dense fluid on the top of the slope. The flow patterns are described and analyzed by the three-layer shallow water equations taken into account the mixing and entrainment processes. The multi-layer shallow water approximation is used, in which a high entrainment zone, where mixing between the dense bottom flow (the core) and ambient fluid occurs, is treated as the intermediate layer. The simple mathematical model describing the evolution of the intermediate turbulent layer in three-layer flow over topography have been developed (Liapidevskii, 2004). Within the model the entrainment rate of fluid from the homogeneous layer can be found by the energy consideration without employing any empirical functions. The analytical solution gives the boundaries and intensity of the mixing layer in a steady-state flow over an incline as well as the nonstationary structure of the density flow head. After the lower boundary of the mixing layer approaches the bottom, entrainment in the bottom layer deceases abruptly and vertical mass transfer from the bottom layer is only due to wave instability of the interface and roll wave generation (Boudlal & Liapidevskii, 2002). The well-known hypothesis on the density current head velocity