The three-body scattering problem with finite pair potentials for one-dimensional case is investigated. The asymptotic function χ₀, which satisfies the three-body Schrödinger equation in whole configuration space outside of compact domain Ω., where the supports of all three pair potentials cross each other, has been presented in a mathematically rigorous way. For large distances |x| → ∞ the function Xo determines the asymptotics of the solution up to the circular wave with smooth coefficient in whole configuration space. The method is based on analogies between fewbody scattering problem and diffraction one of the plane wave on the system of half-transparent infinite screens. Presented here formalism are believed to be useful also for the few-body scattering problem of higher dimensions.