The magma-water interaction in closed systems was studied by a lumped-parameter model which employs the conservation of mass and balance of energy equations for magma, water, and gas (water vapor). The resulting system of ordinary differential equations models the distributions of system pressure, gas volume, water droplet size, and magma, water, and gas temperatures as a function of time and system parameters. The system parameters include the characteristics of the surrounding rocks and degrees of magma and water fragmentation as specified by the initial water and magma drop sizes. The resulting model was applied to the rupturing of lava tunnels at Etna and magma-water interaction in the magmatic conduit of Vesuvius during the gray eruption phase in A.D. 79. The results demonstrate that very rapid system pressurization times of the order of a tenth of a second are possible when the water and magma are highly fragmented. The magma-water interaction within the conduit the Vesuvius was associated with the water inflow into the conduit due to the decrease of the magmatic pressure below the hydrostatic pressure of the surrounding aquifer and fracturing of the conduit wall. The predicted times of pressure increase within the conduit and the high pressure achieved are consistent with observations of phreatomagmatic eruptions and characteristics of the deposits which suggest that these eruptions are characterized by a series of eruptive pulses associated with the transition between magmatic and hydromagmatic phases. ¿ American Geophysical Union 1993