The main objective of the present paper is to show an effect of pressure-dependency of the yield criterion on the development of the plastic zone and the distribution of residual stresses in a thin annular disk subject to a pressure over its inner edge during the loading stage. The Drucker–Prager yield criterion is adopted to account for the effect of the hydrostatic pressure on plastic yielding. The state of stress is supposed to be plane and the material model is perfectly plastic. A semi-analytical stress solution to the problem formulated is given and its qualitative features are emphasized. It is shown that the pressure at which plastic yielding starts and the pressure at which the entire disk becomes plastic are weakly affected by the pressure-dependency of the yield criterion. On the other hand, this dependency has a significant effect on the maximum possible pressure that can be supported by the disk. The minimum pressure at which reverse yielding occurs is also affected by the pressure-dependency of the yield criterion. In general, the residual radial stress distribution is more influenced by the pressure-dependency of the yield criterion than the residual circumferential stress distribution, although the magnitude of circumferential stresses is larger than the magnitude of radial stresses. On the other hand, the effect of pressure-dependency of the yield criterion on the residual circumferential stress distribution is pronounced in the vicinity of the inner edge of the disk, where this stress is important for improving fatigue performance of structures.