Here we address a theoretical analysis of the effects of applied hydrostatic pressure on electron states in concentric GaAs–(Ga,Al)As double quantum rings, under axial magnetic fields. Emphasis is put on the dependence of such effects on the system geometry confinement described within a hard potential model and following an effective-mass approximation. The energy of the ground and excited electronic states were found to decrease with the applied hydrostatic pressure, due mainly to an effective reduction in the barrier potential confinement. Also, while the increase in the magnetic field opens the electron states degeneracy with different angular momenta, the increase in the applied hydrostatic pressure does not alter significantly the energy of these states. For both symmetric and asymmetric double quantum rings, one found that the electron-heavy hole transition energies augment with the applied hydrostatic pressure, mainly due to the increase in the GaAs gap.