Information on snowpack stability, i.e., on the propensity for failure initiation and crack propagation in a weak layer, is essential for forecasting snow avalanches. To complement field observations, snow cover modelling provides information otherwise unavailable on the present and future state of the snow cover, and can be used to evaluate snowpack stability. The main goal of this paper is to summarize the broad spectrum of models to assess snowpack stability from simulated snow profiles. The basic mechanical concepts behind these stability models include: the maximum stress criterion which characterizes the failure initiation propensity and the critical crack length to evaluate the crack propagation propensity. However, many subtle differences between models, mainly due to additional expert rules or the effective implementation of the concepts, can be confusing. We try to disentangle this diversity in this summary. We discuss the differences and also present an overview of the mechanical parameterizations of snow material properties such as strength or stiffness as they are a key ingredient for stability modelling. In addition, we apply the stability models to typical and simplified snow profiles in order to illustrate the influence of the underlying assumptions and the model sensitivity to the mechanical input. As we point out scientific challenges and model limitations, the examples we discussed can provide guidance on the interpretation of similar model results. Moreover, we draw some guiding lines for future research concerning snowpack stability assessment based on snow cover modelling.