Angular averaging of Ewald sums eliminating the nonphysical cubic symmetry of electrostatic field in the uniform ionic system under conditions of computer simulation with periodic boundaries is proposed. The resulting effective potential is central, has simple analytical form and its range is correspondent to the main box size. The approach provides a fast method for computation of electrostatic contribution to the energy of ionic fluids and other dense, uniform Coulomb systems in Monte Carlo or molecular dynamics computer simulation. (C) 2003 American Institute of Physics.