The application of numerical methods to model snow avalanches is of vital importance since in recent years there has been a notable increase in people exposed to risk areas due to the practice of mountain sports. The creation of tools capable of forecasting and simulating avalanches represents a step forward in minimizing the personal and economic costs caused by these natural disasters. With the collaboration of the Institut Flumen and the hydraulic modelling software Iber, it has been possible to develop a valid application for the simulation of snow avalanches using finite volumes. On account of this, the friction terms of the Saint Venant equations were previously modified to be valid for describing the behaviour of these non-Newtonian fluids. This Thesis analyses the parameters of friction, cohesion and slope to study how they affect the descent of avalanches. In addition, the numerical scheme is extended by incorporating the parameter of entrainment and four equations are developed that depend, independently, on velocity, snow height and bed shear stress. Thenceforth, the model is calibrated, and the equations are compared taking into account the field data of an avalanche registered in the area of Vallter, located in the Pyrenees of Girona. Finally, once the model has been determined to be sufficiently robust, the event of a historical avalanche that occurred in the ancient village of Àrreu -Pyrenees of Lleida- where nineteen inhabitants lost their lives is studied. For the first time, a study is proposed on how this fateful event happened, taking into account the existing historical documentation, and different current methods of protection and containment are proposed to prevent it from happening again.