The disturbance of the light conductivity in optical fiber transporting intense laser radiation leads to the occurrence of brightly illuminated laser plasma region. Plasma begins to move towards radiation, irreversibly damaging the optical fiber. Depending on the intensity of the laser energy, different rates of propagation of damage along the optical fibers towards the radiation are possible. This is either "combustion" of optical fibers, or "optical detonation". Both of these processes -"combustion" and "optical detonation" of optical fibers -destroy the light conductivity of silica fibers along the entire length. The rate of propagation of "combustion" depends on the energy density and is several meters per second. The detonation-like mode of destruction extends with velocity of several kilometers per second. Shock-wave data of silica fiber materials are necessary for modeling of the of such destruction process. In this paper the experimental study of propagation of the shock wave front in the materials of the optical fibers core in explosive experiments was carried out for the first time. For study of the detonation-like mode of a laser discharge propagation, experimental fibers were produced by the Fiber Optics Research Center of the Russian Academy of Sciences (FORC RAS) and an available industrial communication fiber (SMF-28e single-mode fiber from Corning). In the shock wave experiment, a two-wave mode of the propagation of the shock wave is confirmed. Anomalous compressibility behind the front of the shock wave was found in the materials of the optical fiber. The decrease in the sound velocity was about one km/s.