The complex shear modulus of fresh and thermally damaged porcine liver has been measured, in vitro, using an ultrasonic shear wave imaging technique. Measurements were compared to two constitutive models, Kelvin-Voigt and Zener, to estimate the complex modulus of liver for shear wave frequencies between 50 and 300 Hz. An axially vibrated needle placed in the liver excites harmonic shear waves that are imaged using a pulsed Doppler technique. Liver heated to 47°C for 90 min was found to have little measurable cellular damage, and yet the elastic shear modulus increased by a factor of two and the viscous shear modulus increased by a factor of three in this frequency range. These observations imply that elastic properties, especially the viscous shear modulus, may be a sensitive indicator of thermal damage. Also, within the testing bandwidth for shear waves, the Zener model represented the data better than the Kelvin-Voigt model.