Barium stars are extrinsic Asymptotic Giant Branch (AGB) stars. They present the s-enhancement characteristic for AGB and post-AGB stars, but are in an earlier evolutionary stage (main sequence dwarfs, subgiants, red giants). They are believed to form in binary systems, where a more massive companion evolved faster, produced the s-elements during its AGB phase, polluted the present barium star through stellar winds and became a white dwarf. The samples of barium stars of Allen & Barbuy (2006) and of Smiljanic et al. (2007) are analysed here. Spectra of both samples were obtained at high-resolution and high S/N. We compare these observations with AGB nucleosynthesis models using different initial masses and a spread of 13C-pocket efficiencies. Once a consistent solution is found for the whole elemental distribution of abundances, a proper dilution factor is applied. This dilution is explained by the fact that the s-rich material transferred from the AGB to the nowadays observed stars is mixed with the envelope of the accretor. We also analyse the mass transfer process, and obtain the wind velocity for giants and subgiants with known orbital period. We find evidence that thermohaline mixing is acting inside main sequence dwarfs and we present a method for estimating its depth.