The epsilon-modified Poisson-Boltzmann (epsilon-MPB) equations (J. Phys. Chem. B, 2007, 111, 5264) have been solved on a three-dimensional grid for an all-atom geometry model of B-DNA. The approach is based on the implicit solvent model including finite sizes of hydrated ions and a dielectric approximation of the ion hydration shell. Results were obtained for the detailed geometry model of B-DNA in dilute and moderately concentrated solutions of NaCl and CaCl2. All epsilon-MPB parameters of ions and dielectric medium were extracted from published results of all-atom molecular dynamics simulations. The study allows evaluations of the ion size, interionic correlation, and the solvent dielectric saturation effects on the ion distributions around DNA. It unambiguously suggests that the difference between the epsilon-MPB and Poisson-Boltzmann distributions of ions is low for Na+ counterions. Such a difference in the case of divalent counterions Ca2+ is dramatic: the dielectric saturation of the ion hydration shell leads to point-like adsorption of Ca2+ on the phosphate groups of DNA. The epsilon-MPB equations were also applied to calculate the energy of interaction between two B-DNA molecules. Results agree with previously published simulations and experimental data. Some aspects of ion specificity of polyelectrolyte properties are discussed.