Pressure-shear plate impact experiments are used to study the nonlinear dynamic response of an epoxy and a vinyl ester at shearing rates of 10(5) - 10(6) s(-1). Samples with thicknesses in the range 10/mu m - 100 mu m are formed between two hard steel plates. Because of its higher wave speed, the longitudinal wave generated at impact reaches the sample first and, after a few reverberations through the thickness of the sample, subjects the sample to a state of uniaxial strain compression. Once the sample is fully compressed the shear wave arrives and imposes a simple shearing deformation. From the transverse velocity, measured interferometrically at the rear surface of the sandwich target, the shear stress and the transverse velocity at the rear surface of the sample are determined. These measurements provide an indication of the shearing resistance of the material under pressure. Because the sample bonds to the bounding plates, the shearing of the sample continues even after longitudinal unloading waves arrive from the rear surface of the target and reduce the nominal pressure in the sample to zero. Thus, from a single experiment, one obtains the response of the sample in simple shear - both under pressure and without pressure. From such experiments a pressure-sensitivity of inelastic shearing resistance is found for both the epoxy and two vinyl esters.