Accelerator-based γ-ray-induced positron annihilation spectroscopy performs positron annihilation spectroscopy by utilizing MeV bremsstrahlung radiation generated from an accelerator (We have named the technique “accelerator-based γ-ray-induced PAS,” even though “bremsstrahlung” is more correct here than “γ rays”. The reason for that is to make the name of the technique more general, since PAS may be performed by utilizing MeV γ rays emitted from nuclei through the use of accelerators as described later in this article and as in the case of positron lifetime spectroscopy [F.A. Selim, D.P. Wells, and J.F. Harmon, Rev. Sci. Instrum. 76, 033905 (2005)].) instead of using positrons from radioactive sources or positron beams. MeV γ rays create positrons inside the materials by pair production. The induced positrons annihilate with the material electrons emitting a 511-keV annihilation radiation. Doppler broadening spectroscopy of the 511-keV radiation provides information about open-volume defects and plastic deformation in solids. The high penetration of MeV γ rays allows probing of defects at high depths in thick materials up to several centimeters, which is not possible with most of the current nondestructive techniques. In this article, a detailed description of the technique will be presented, including its benefits and limitations relative to the other nondestructive methods. Its application on the investigation of plastic deformation in thick steel alloys will be shown.