By using a combination of atomic force and confocal microscopy, we explore the effect of 1:1 electrolyte (NaCl) on the stiffness of polyelectrolyte microcapsules. We study the "hollow" and "filled" (with polystyrene sulfonate) capsules. In both cases the shells are composed of layers of alternating polystyrene sulfonate (PSS) and polyallylamine hydrochloride (PAH). The stiffness of both "hollow" and "filled" capsules was found to be largest in water. It decreases with salt concentration up to approximately 3 mol/L and gets quasi-constant in more concentrated solutions. The "filled" capsules are always stiffer than "hollow." The observed softening correlates with the salt-induced changes in morphology of the multilayer shells detected with the scanning electron microscopy. It is likely that at concentrations below approximately 3 mol/L the multilayer shell is in a "tethered" state, so that the increase in salt concentration leads to a decrease in number of ionic cross-links and, as a result, in the stiffness. In contrast, above the critical concentration of approximately 3 mol/L multilayer shells might be in a new, "melted," state. Here the multilayer structure is still retained, but sufficient amount of ionic cross-links is broken, so that further increase in salt concentration does not change the capsule mechanics. These ideas are consistent with a moderate swelling of multilayers at concentrations below approximately 3 mol/L and significant decrease in their thickness in more concentrated solutions measured with surface plasmon spectroscopy.