Estimation of soft tissue elasticity is of interest in several clinical applications. For instance, tumors and fibrotic lesions are notoriously stiff compared with benign tissue. A fully quantitative measure of lesion stiffness can be obtained by shear wave (SW) elastography. This method uses an acoustic radiation force to produce laterally propagating SWs that can be tracked to obtain the velocity, which in turn is related to Young's modulus. However, not only elasticity, but also viscosity plays an important role in the propagation process of SWs. In fact, viscosity itself is a parameter of diagnostic value for the detection and characterization of malignant lesions. In this paper, we describe a new method that enables imaging viscosity from SW elastography by local model-based system identification. By testing the method on simulated data sets and performing in vitro experiments, we show that the ability of the proposed technique to generate parametric maps of the viscoelastic material properties from SW measurements, opening up new possibilities for noninvasive tissue characterization.