Using a VISAR laser interferometer, the experiments on investigation of the shock wave structure, spall strength and determination of Hugoniot parameters were performed for two composite materials based on the aramid fibers. Textolite and Kevlar were made using the same epoxy resin and aramid fibers, but had a different structure - unidirectional fibers and plies of woven fibers, respectively. The density of these materials is approximately 1.27 g/cm3. To study the shock wave compressibility of composite materials under high pressure, the explosive propellant charges were used to provide a flat throw of aluminum flyer plates with velocities from 0.7 to 5.05 km/s. As a result of experiments, particle velocity profiles on the composite/water boundary were obtained. On the velocity profiles for kevlar and textolite with transverse orientation of the fibers, after the initial shock jump, oscillations are observed due to the heterogeneous structure of the investigated materials. Unlike the composite materials with transverse orientation of the fibers, in the case when a shock wave propagates along the fibers, a two-wave configuration is recorded, which is due to the anisotropic structure of material. It was found that Hugoniots of composites with perpendicular orientation of the fibers are parallel to each other and differ only in the first coefficient determined by the sound speed of the material. Also a study of spall strength of textolite and Kevlar was performed. It was found for both materials that the value of spall strength along the fibers is higher than that for the transverse direction.