An axisymmetrical numerical model has been developed in order to find the temporal evolution of pressure, the position of the exsolution level, the velocity field, the eruption rate, and the amount of erupted material of a shallow, volatile‐rich, felsic magma chamber during a Plinian central vent eruption. The overpressure necessary to trigger the eruption is assumed to result from crystallization‐driven volatile oversaturation. We solve the resulting set of equations using a finite element method. The results obtained show that the pressure at the conduit entrance decreases exponentially as the eruption proceeds. This produces a shifting of the exsolution level, so that deeper parts of the chamber become progressively volatile oversaturated during the eruption. We assess the influence of chamber geometry and the physical properties of the magma on the computed parameters using several numerical examples. The results are also compared with those predicted by previous models from the literature and are found to be in good agreement with documented eruptions. The model constitutes a first attempt to numerically model the dynamics and the temporal evolution of the most relevant physical parameters during withdrawal from a closed magma chamber.