The objective of this study was to assess the potential for noninvasively identifying viscoelastic material properties in arterial vessels using ultrasound radiation force and modern computational inverse problem techniques. A rubber tube embedded in gelatin was excited at different points along the axis using impulsive ultrasound radiation force. The resulting mechanical waves were measured using a laser vibrometer and pulse-echo ultrasound. The inverse problem was cast as an optimization problem, in which the discrepancy between the measured dynamic response and the computed finite element model response was minimized with respect to viscoelastic material parameters. The model was very sensitive to the tube’s viscoelastic parameters and relatively insensitive to those of the gelatin. The viscoelastic properties of the tube obtained from the inverse problem were compared to the results obtained from a dynamic mechanical analyzer (DMA). For the overlapping range of frequencies (130–190 Hz), the results of the inverse problem gave an equivalent modulus that range from 7.3–8.5 MPa, while the DMA values range from 6.0–9.2 MPa. These results have important implications for using ultrasound radiation force in noninvasive characterization of the viscoelastic properties of arteries in vivo. [This work was supported in part by Grant No. EB002640 from NIH.]