The angular momentum projected Generator Coordinate Method, with the quadrupole moment as collective coordinate and the Gogny force as the effective interaction, is used to describe the properties of the ground state and low‐lying excited states of the even‐even Magnesium isotopes20–40Mg. It is found that the ground states of the N=2032Mg and N=2840Mg nuclei are deformed and therefore the corresponding shell closures are not preserved. Rather good agreement with experimental data for many observables is obtained. © 2003 American Institute of Physics