The numerical formulation of a one-dimensional physical snowpack model is presented. The model is operationally employed on a day-to-day basis by avalanche warners to predict snowpack settlement, layering, surface energy exchange and mass balance. Meteorological data obtained from automatic weather stations positioned near avalanche starting zones is used as model input. In this paper, the one-dimensional equations governing the heat transfer, water transport, vapour diffusion and mechanical deformation of a phase changing snowpack are stated. New snow, wind drift and snow ablation are treated as special mass boundary conditions. Snow is modelled as a three-component (ice, water, air) porous material capable of undergoing large irreversible viscous deformations. Phase changes between the components are simulated. Snow layers are defined not only in terms of height and density, but also microstructure. That is, by the size, shape and bonding of the grains composing the ice lattice. The governing differential equations are solved using a fully implicit Lagrangian Gauss-Seidel finite-element method. Example calculations from the catastrophic avalanche winter 1999 are presented to document model performance. The overall mass balance evaluation shows that the model accurately predicts the build-up and ablation of the seasonal alpine snowcover.