Pressure-shear plate impact (PSPI) experiments conducted to study the mechanical response of polyurea at pressures up to 18 GPa and strain rates of 105-106 s-1 will be reported. These experiments show that the shearing resistance of this block co-polymer increases proportionately with increasing pressure, reaching 1 GPa at a pressure of 18 GPa. This high shearing resistance is remarkable ― greater than that of many high strength steels and at much lower density. A new symmetric pressure-shear plate impact (SPSPI) configuration has been developed in order to enable the direct measurement of the thickness-averaged nominal strain rates of the sample — as well as the tractions on both of its interfaces with linear elastic plates. This enhancement is made possible by using a symmetric configuration for which the velocity of the mid-plane of the sample is known from symmetry to be one-half of the impact velocity. One dimensional elastic wave theory is used to obtain tractions and particle velocities at the sample/anvil interface from the measured rear-surface velocities. In this way, nominal strain-rate histories are obtained for both longitudinal and shear strains. Finite element and molecular dynamics methods are used to model the response. A quasilinear viscoelasticity model is introduced to model the relaxation of shear stresses in these experiments and in a pilot experiment on Teflon. Temperature increases during the PSPI experiments have been shown to be significant, although the ramp-wave-like loading keeps the temperatures much lower than they would be for shock wave loading to the same pressure.