Recent observations of galaxy clusters in radio and X-ray indicate that cosmic rays and magnetic fields may be energetically important in the intracluster medium. According to the estimates based on theses observational studies, the combined pressure of these two components of the intracluster medium may range between $10\%{~}100\%$ of gas pressure, although their total energy is probably time dependent. Hence, these non-thermal components may have influenced the formation and evolution of cosmic structures, and may provide unique and vital diagnostic information through various radiations emitted via their interactions with surrounding matter and cosmic background photons. We suggest that shock waves associated with cosmic structures, along with individual sources such as active galactic nuclei and radio galaxies, supply the cosmic rays and magnetic fields to the intracluster medium and to surrounding large scale structures. In order to study 1) the properties of cosmic shock waves emerging during the large scale structure formation of the universe, and 2) the dynamical influence of cosmic rays, which were ejected by AGN-like sources into the intracluster medium, on structure formation, we have performed two sets of N-body /hydrodynamic simulations of cosmic structure formation. In this contribution, we report the preliminary results of these simulations.