We estimate effects of the final state interactions in B → ππ decays coming from rescattering of ππ via exchange of ρ, σ, f 0 mesons. Then we include the ρρ rescattering via exchange of π, ω, a 1 mesons and finally we consider contributions of the a 1 π rescattering via exchange of ρ. The absorptive parts of amplitudes for these processes are determined. In the case of π + π − decay mode, due to model uncertainties, the calculated contribution is |M A | ≤ 1.7 × 10 −8 GeV. This produces a small relative strong phase for the tree and color-suppressed B → ππ amplitudes consistent with the result of a recent phenomenological analysis based on the BaBar and Belle results for the B → ππ branching ratios and CP asymmetries.