One of the fundamental problems in nucleic acids biophysics is to predict the different forces that stabilize nucleic acid tertiary folds. Here we provide a quantitative estimation and analysis for the forces between DNA helices in an ionic solution. Using the generalized Born model and the improved atomistic tightly binding ions model, we evaluate ion correlation and solvent polarization effects in interhelix interactions. The results suggest that hydration, Coulomb correlation and ion entropy act together to cause the repulsion and attraction between nucleic acid helices in Mg2+ and Mn2+ solutions, respectively. The theoretical predictions are consistent with experimental findings. Detailed analysis further suggests that solvent polarization and ion correlation both are crucial for the interhelix interactions. The theory presented here may provide a useful framework for systematic and quantitative predictions of the forces in nucleic adds folding.