A theoretical model based on a depth-averaged version of two-phase flow equations is developed to describe the initiation of underwater granular avalanches. The rheology of the granular phase is based on a shear-rate-dependent critical state theory, which combines a critical state theory proposed by Roux & Radjai (1998), and a rheological model recently proposed for immersed granular flows. Using those phenomenological constitutive equations, the model is able to describe both the dilatancy effects experienced by the granular skeleton during the initial deformations and the rheology of wet granular media when the flow is fully developed. Numerical solutions of the two-phase flow model are computed in the case of a uniform layer of granular material fully immersed in a liquid and suddenly inclined from horizontal. The predictions are quantitatively compared with experiments by Pailha, Nicolas & Pouliquen (2008), who have studied the role of the initial volume fraction on the dynamics of underwater granular avalanches. Once the rheology is calibrated using steady-state regimes, the model correctly predicts the complex transient dynamics observed in the experiments and the crucial role of the initial volume fraction. Quantitative predictions are obtained for the triggering time of the avalanche, for the acceleration of the layer and for the pore pressure.