This paper introduces a three-dimensional model for simulating dense-snow avalanches, based on the numerical method of cellular automata. This method allows one to study the complex behavior of the avalanche by dividing it into small elements, whose interaction is described by simple laws, obtaining a reduction of the computational power needed to perform a three-dimensional simulation. Similar models by several authors have been used to model rock avalanches, mud and lava flows, and debris avalanches. A peculiar aspect of avalanche dynamics, i.e., the mechanisms of erosion of the snowpack and deposition of material from the avalanche is taken into account in the model. The capability of the proposed approach has been illustrated by modeling three documented avalanches that occurred in Susa Valley (Western Italian Alps). Despite the qualitative observations used for calibration, the proposed method is able to reproduce the correct three-dimensional avalanche path, using a digital terrain model, and the order of magnitude of the avalanche deposit volume.