Structures developing above long‐term growing shallow‐level magma reservoirs, such as resurgent domes, may contain information on the reservoir itself. To understand the formation of such tectonic features, we have investigated the deformation process around a shallow pressurized magma reservoir embedded in a damaging elastic volcanic edifice. Our model allows evidencing the effect of the progressive damage in producing the fault pattern associated to tectonic surface deformation. Damage is first isotropic around the cavity and constitutes a damaged zone. Then the free‐surface effect appears and an anisotropic shear strain develops from the boundary of the damaged zone; it localizes on reverse faults that propagate upward to the surface. When the surface deformation is sufficient, normal faulting appears. Finally, the complete structure shows an undeformed wedge above the damaged zone. This structure is similar to those found by analogue modelling and from field geologic observations. From this model, we found a relation to estimate the reservoir radius and depth from the graben and dome widths. From limit analysis, we deduced an analytical expression of the magma reservoir pressure which provides a better understanding of the magma pressure build‐up during doming. The dip of reverse faults limiting the dome can be inferred from the minimal pressure required to rupture the crust around the reservoir. Finally, the magma reservoir overpressure, the dip of the faults, the reservoir depth and the damaged zone radius is inferred from three parameters: the ratio ρR computed from the dome and graben widths, the cohesion and the friction angle.