The effects of hydrostatic stress on the density of donor impurity states and donor-related optical absorption spectra in a GaAs–(Ga,Al)As quantum well are investigated. The shallow-donor binding energy for different well widths and different values of the hydrostatic stress has been calculated. It has been found that for wider well widths the binding energy increases slowly with hydrostatic stress contrary to the behavior of the binding energy for wells with smaller widths. In particular, it has been found that the binding energy does not change appreciably with the impurity position when the width of the well is small and for large values of hydrostatic stress. Two structures in both the density of states and the optical absorption spectra, associated with impurities located close to the center and to the edges of the structure, are obtained. Also, it has been observed that the density of states and the optical absorption spectra depend strongly on the applied hydrostatic stress.