Abstract We develop a model for explosive eruptions in cylindrical conduits generated by plug disruption at the top of the conduit. The eruption is calculated for a standard set of parameters for rhyolite. The model takes into account temperature variations and non-Newtonian magma rheology. We analyzed the influence of principal parameters such as fragmentation criteria, magma rheology, and initial conditions. We conclude that the variation of magma temperature is less than 70 K during eruption, and the model with bubble concentration-dependent viscosity leads to the increase of the steady discharge rate by about 40%. The eruption model is extended to include interaction between magma in the conduit and water in a surrounding aquifer. The phreatomagmatic eruption is also initiated by plug disruption. Two cases of initial aquifer pressure are considered: magmastatic and hydrostatic. These cases are valid for confined and unconfined aquifers. For the first case (confined aquifer), water influx influences the conduit flow soon after plug disruption and leads to the additional peaks of discharge rate; for the second case (unconfined aquifer), a purely magmatic, explosive eruption of longer duration is followed by a phreatomagmatic phase. In both cases, magma discharge rate increases by 10–100% in comparison with purely magmatic eruption.