The reaction of alpine glaciers to shifts in the equilibrium line altitude (ELA) is calculated by using a two-dimensional numerical model to solve the full equations for the velocity and stress fields (full-system model) in the absence of basal motion. Rates of advance and retreat of the snout of typically sized alpine glaciers are found to be insensitive to the details of the flow at the snout, even when the glaciers are far from steady state. A comparison of results obtained with a full-system model and a shallow ice approximation (SIA) model yields no significant differences in advance or retreat rates. This assumption has been implicitly made in numerous previous climatic studies and is here shown to be well justified. Using a realistic mass balance altitude feedback, only slight model-dependent changes in steady state lengths are found. The relative importance of mass balance and glacier dynamics for the transient response of alpine glaciers to changes in the ELA is given a precise meaning by determining the model-dependent additional shifts in ELA needed for the SIA and the full-system models to produce identical changes in length. For alpine glaciers, these additional shifts in ELA are on the order of 10 m, which is within the error range of ELA estimates. It follows that at least in the absence of significant basal motion, there is no need to include the effects of horizontal stresses when calculating the reaction of alpine glaciers to climatic changes. Attention should focus on accurate determination of the mass balance distribution and model tuning to give realistic ice thickness distributions.