The effect of the ionic charge on the ionic distribution around a simple B-DNA model at the continuum solvent level is investigated using Monte Carlo simulation. In the model, the DNA shape is approximated by a set of simple geometric elements with charges at the canonical phosphate positions. Three series of simulations for an infinitely diluted polyion with added salt have been carried out. In each of them the ionic strength is kept constant. At low ionic strength, the behavior of monovalent, divalent, and trivalent cations is studied. It is shown that the number of counterions within the grooves depend only weakly on its valence so the fraction of DNA charge canceled out at small distances increases with the charge of the cation. This results in a deeper penetration of the coions, which, for systems with highly charged counterions as a 3:1 salt, may even surpass the bulk concentration in the vicinity of the polyelectrolyte. Nevertheless, no overscreening of the DNA charge has been observed in this system. On the contrary, the charge reversal phenomenon appeared in the simulations at high ionic strength irrespective of the ionic valences. It seems that this feature occurs when the bulk concentration of the mobile ions is of the same order as the local concentration in the vicinity of DNA with no added salt. Finally, the competition between monovalent and divalent cations is studied at concentrations close to those of biological media. It is shown that the divalent cations push the monovalent ions out of the DNA surroundings even if their concentration is much lower. (C) 2001 American Institute of Physics.