The binding energy of shallow hydrogenic impurities in spherical quantum dots in the influence of pressure is calculated using a variational approach within the effective mass approximation. The binding energy is computed for GaAs/Ga 1− x Al x As structures as a function of the dot size. The results show that the impurity binding energy (i) increases with the reduction in dot sizes for a given pressure (ii) increases with the pressure is increased for a given dot (iii) the energy increases to a maximum value at 50 Å and then decreases as the size of the dot increases beyond 50 Å when the realistic model is considered and (iv) the ionization energies are higher as the pressure becomes stronger. All the calculations have been carried out with finite and infinite models and the results are compared with available data in the literature.