The tetragonal PbWO4 (PWO) is one of the most important scintillating crystals, being used both in the Compact Muon Solenoid (CMS) experiment at the European Organization for Nuclear Research (CERN) and in the PANDA project at the Facility for Antiproton and Ion Research (FAIR). Light yield and other relevant scintillation properties depend, among many factors, also on the crystal mechanical quality. Accordingly, a detailed knowledge of crystal piezo-optic properties is a mandatory step toward understanding elasto-optic behavior and performing crystal quality control. In this paper, we evaluate for the first time, to the best of our knowledge, by means of both photoelastic and x-ray measurements, some components of the piezo-optic tensor; moreover, when the crystal is acted upon by a uniaxial stress, we obtain an evaluation for the rotation angle of the optic plane under stress as well as the photoelastic constant. These parameters are necessary to detect the residual stresses within the crystal, if any, and to give an overall quality measure. Such a methodology is in general suitable for any tetragonal crystals.