Simple analytical models of subglacial eruptions are presented, which simulate evolving subglacial cavities and volcanic edifices during rhyolitic eruptions beneath temperate glaciers. They shove that the relative sizes of cavity and edifice may strongly influence the eruption mechanisms. Intrusive eruptions will occur if the edifice fills the cavity, with rising magma quenched within the edifice and slow melting of ice. Explosive magma-water interaction may occur if a water- or steam-filled gap develops above the edifice. Meltwater is assumed to drain away continuously, but any gap above the edifice will be filled by meltwater or steam. Ductile roof closure will occur if the glacier weight exceeds the cavity pressure and is modelled here using Nye's law. The results show that the effusion rate is an important control on the eruption style, with explosive eruptions favoured by large effusion rates. The models are used to explain contrasting eruption mechanisms during various Quaternary subglacial rhyolite eruptions at Torfajokull, Iceland. Although the models are simplistic, they are first attempts to unravel the complex feedbacks between subglacial eruption mechanisms and glacier response that can lead to a variety of eruptive scenarios and associated hazards.