Shock waves form in the intergalactic space as an ubiquitous consequence of cosmic structure formation. Using N-body/hydrodynamic simulation data of a ACDM universe, we examined the properties of cosmological shock waves including their morphological distribution. Adopting a diffusive shock acceleration model, we then calculated the amount of cosmic ray energy as well as that of gas thermal energy dissipated at the shocks. Finally, the dynamical consequence of those cosmic rays on cluster properties is discussed.