Using a simple model for the onset of solar eruptions, we investigate how an existing magnetic configuration containing a flux rope evolves in response to new emerging flux. Our results show that the emergence of new flux can cause a loss of ideal MHD equilibrium under certain circumstances, but the circumstances which lead to eruption are much richer and more complicated than one might expect given the simplicity of the model. The model results suggest that the actual circumstances leading to an eruption are sensitive not only to the polarity of the emerging region, but also to several other parameters, such as the strength, distance, and area of the emerging region. It has been suggested by various researchers that the emergence of new flux with an orientation which allows reconnection with the preexisting flux (a process sometimes referred to as tether cutting) will generally lead to destabilization of the coronal or prominence magnetic field. Although our results can replicate such behavior for certain restricted classes of boundary conditions, we find that, in general, there is no simple, universal relation between the orientation of the emerging flux and the likelihood of an eruption. ¿ 2001 American Geophysical Union