The statistical modelling of gravitational avalanche-type processes is carried out using the Monte Carlo method. The process of snow avalanche origin is described with the model of stress state and stability of snow cover on a slope. The statistical simulation of the stress state of a snow slab is performed for avalanche site No. 22 (Khibiny, Russia). The strength characteristics of the snow slab are considered as randomvariables.The influence of the first moments of the distributions of the

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... b-strength parameters on the probability of avalanche release is studied. Using a hydraulic model of a dense flow avalanche, the statistical modelling of avalanche dynamics for the avalanche site "Domestic" (Elbrus region, Russia) is carried out. The coefficients of dry and turbulent friction and snow entrainment are considered as random parameters of the model. The histograms and distribution functions of the run-out distance, thickness and volume of avalanche depositions are obtained. The model and empirical distribution functions of the avalanche run-out distance are compared. Statistical simulation of slushflow dynamics (basin of Bear brook, Khibiny, Russia) is performed. The two-layer deterministic model of slushflow is used. The random parameters of the model assumed are: the water inflow on the "tail"of the flow and the coefficient of dry friction for slush. The histograms and distribution functions of dynamic characteristics of flow are obtained. The model outcomes are compared with field data.