Caldera eruptions are among the most hazardous of natural phenomena. Many calderas around the world are active and are characterised by recurrent uplift and subsidence periods due to the dynamics of their magma reservoirs. These periods of unrest are, in some cases, accompanied by eruptions. At Campi Flegrei caldera (CFc), which is an area characterised by very high volcanic risk, the recurrence of this behaviour has stimulated the study of the rock rheology around the magma chamber, in order to estimate the likelihood of an eruption. This study considers different scenarios of shallow crustal behaviour, taking into account the earlier models of CFc ground deformation and caldera eruptions, and including recent geophysical investigations of the area. A semi-quantitative evaluation of the different factors that lead to magma storage or to its eruption (such as magma chamber size, wall-rock viscosity, temperature, and regional tectonic strain rate) is reported here for elastic and viscoelastic conditions. Considering the large magmatic sources of the CFc ignimbrite eruptions (400–2,000 km3) and a wall-rock viscosity between 1018 and 1020 Pa s, the conditions for eruptive failure are difficult to attain. Smaller source dimensions (a few cubic kilometres) promote the condition for fracture (eruption) rather than for the flow of wall rock. We also analyse the influence of the regional extensional stress regime on magma storage and eruptions, and the thermal stress as a possible source of caldera uplift. The present study also emphasises the difficulty of distinguishing eruption and non-eruption scenarios at CFc, since an unambiguous model that accounts for the rock rheology, magma-source dimensions and locations and regional stress field influences is still lacking.