The sensitivity of Vatnajokull ice cap, Iceland, to perturbations in equilibrium line altitude (ELA) is analyzed by performing a series of model experiments using a shallow ice approximation (SIA) flow model. For this purpose a simple but realistic parameterization for the mass balance is used that accurately simulates the observed variability in surface mass balance over a period of nine years. We find that because of feedback between mass balance and altitude the ice cap either grows without bounds or settles to steady states depending on whether ELA is larger or smaller than a critical value ELA crit The largest modeled steady state is 60% of the current volume of the ice cap. The ice cap, as modeled, is therefore currently not close to a possible stable steady state. Past climate history and spatial and temporal variations in basal condition, such as surges, can be expected to have an influence on the ice cap and have to be taken into account when modeling the response of the ice cap to future climate change scenarios. For the neighboring ice cap, Hofsjökull, the relationship between ELA and volume is, in contrast, found to be simple, and Hofsjökull is close to a stable steady state with respect to the current climatic conditions. Introducing surges, which is not done here, will likely change the details of the ELA-volume relationship of Vatnajökull, presumably by making the relationship between volume and ELA more complex, and possibly less sensitive, as a further nonlinear feature is added to the model.