Values of complex shear compliance (and rigidity) have been obtained for a sample of polyisobutylene of viscosity-average molecular weight 1.35×106 at 22 temperatures from −45 to 100°C and at about 20 frequencies from 30 to 5000 cps. Measurements were made by means of the transducer method of Fitzgerald and Ferry with a precision of ±2 percent and are estimated to be accurate to within ±3 percent as evidenced by agreement obtained between 7 different samples of widely varying dimensions. Values of the real part of the complex shear compliance J′ vary from 3.1×10−7 cm2/dyne at 99.9°C to 1.0×10−10 cm2/dyne at −44.6°C. The frequency dependence of the loss tangent J″/J′ indicates the presence of a low, broad maximum of 1.7 at −10 to −5°C and a second, smaller maximum at lower temperatures. This second maximum is also evident in a plot of J″/J′ at a fixed frequency against temperature. The wide temperature and frequency ranges of the measurements have provided an essentially complete experimental description of the dispersion region in polyisobutylene corresponding to the transition from a rubber-like elasticity to that of a hard glass.