Spin relaxation has been measured at 3 kOe and at lattice temperatures from 1.24° to 250°K for theE′ centers generated in one type of vitreous silica by 2‐MeV gamma rays. An unusual temperature dependence was found in which the spin‐lattice relaxation time varies roughly asT−2,5over most of the range. All of the data are accurately fitted by analytical functions derived from a coupling of the individual defect centers to the vitreous host involving excess local strain due to mechanical resonances of about 4.1×1011and 6.0×1012cps at eachE′ center. The strength of the coupling and the characteristic frequencies of mechanical resonance are similar to those in crystalline SiO2.