Rhyolite eruptions in Iceland mostly take place at long-lived central volcanoes, examples of which are found associated with each of the present-day rift-zone ice caps. Subglacial eruptions at Kerlingarfjöll central volcano produced rhyolite tuyas that are notable for their exposures of early-erupted pyroclastic material. Observations from a number of these edifices are synthesised into a general model for explosive rhyolite tuya formation. Eruptions begin with violent phreatomagmatic explosions that generate massive tuff (mT), but the influence of water quickly declines, leading to the formation of massive lapilli-tuffs (mLT) containing magmatically-fragmented vesicular pumice and ash. These are deposited rapidly near the vent, probably by moist pyroclastic density currents, confined by ice but not within a meltwater lake. The explosive-effusive transition is controlled by the ascent rate and gas content of the magma. An unusual obsidian-rich massive lapilli-tuff lithofacies (omLT) is identified and interpreted as pyroclastic material that was intruded into gas-fluidised deposits at the explosive-effusive transition. The effusive phase of eruption involves the emplacement of intrusions and lava caps. Intrusions of lava into the early-erupted phreatomagmatic deposits are characterised by peperitic margins and the formation of hyaloclastite. Intrusions into stratigraphically higher levels of the pyroclastic material show more limited interaction with the host tephra and have microcrystalline cores. Large lava bodies with columnar-jointed margins cap the tuyas and have intrusive basal contacts with the tephras. The main influence of the ice is to confine the rhyolite eruptive products to immediately above the vent region. This is in contrast to subglacial basaltic tuya-forming eruptions, which are characterised by the formation of meltwater lakes, phreatomagmatic fragmentation and subaqueous deposition. The lack of meltwater storage may reduce the potential for large jökulhlaups.