Asymptotic Giant Branch (AGB) stars play a fundamental role in s-process nucleosynthesis during their thermal pulsing phase. The theoretical predictions obtained by AGB models at different masses, s-process efficiencies, dilution factors and initial r-enrichment, are compared with spectroscopic observations of Carbon-Enhanced Metal-Poor stars enriched in s-process elements, CEMP(s), collected from the literature. We discuss here five stars as example, CS 22880-074, CS 22942-019, CS 29526-110, HE 0202-2204 and LP 625-44. All these objects lie on the main sequence or on the giant phase, clearly before the thermally pulsing AGB stage. The hypothesis of mass transfer from an AGB companion, would explain the observed s-process enhancement. CS 29526-110 and LP 625-44 are CEMP(s + r) objects, and are interpreted assuming that the molecular cloud, from which the binary system formed, was already enriched in r-process elements by SNII pollution. In several cases, the observed s-process distribution may be accounted for by AGB models of different initial masses with proper ¹³C-pocket efficiencies and dilution factors. Na (and Mg), produced via the neutron capture chain starting from ²²Ne, may provide an indicator of the initial AGB mass.