Presented here are the results of a systematic study of the viscoelastic properties of polyurea over broad ranges of strain rates and temperatures, including the high-pressure effects on the material response. Based on a set of experiments and a master curve developed by Knauss (W.G. Knauss, Viscoelastic Material Characterization relative to Constitutive and Failure Response of an Elastomer, Interim Report to the Office of Naval Research (GALCIT, Pasadena, CA, 2003.) for time-temperature equivalence, we have produced a model for the large deformation viscoelastic response of this clastomer. Higher strain-rate data are obtained using Hopkinson bar experiments. The data suggest that the response of this class of polymers is strongly pressure dependent. We show that the inclusion of linear pressure sensitivity successfully reproduces the results of the Hopkinson bar experiments. In addition, we also present an equivalent but approximate model that involves only a finite number of internal state variables and is specifically tailored for implementation into explicit finite-element codes. The model incorporates the classical Williams-Landel Ferry (WLF) time-temperature transformation and pressure sensitivity (M.L. Williams, R.F. Landel, and J.D. Ferry, J. Am. Chem. Soc., 77 3701 (1955)), in addition to a thermodynamically sound dissipation mechanism. Finally, we show that using this model for the shear behaviour of polyurea along with the elastic bulk response, one can successfully reproduce the very high strain rate pressure-shear experimental results recently reported by Jiao et al. (T. Jiao, R.J. Clifton and S.E. Grunschel, Shock Compression of Condensed Matter 2005 (American Institute of Physics, New York, 2005.).