CEMP-s stars are very metal-poor stars with enhanced abundances of carbon and s-process elements. They form a significant proportion of the very metal-poor stars in the Galactic halo and are mostly observed in binary systems. This suggests that the observed chemical anomalies are due to mass accretion in the past from an asymptotic giant branch (AGB) star. Because CEMP-s stars have hardly evolved since their formation, the study of their observed abundances provides a way to probe our models of AGB nucleosynthesis at low metallicity. To this end we included in our binary evolution model the results of the latest models of AGB nucleosynthesis and we simulated a grid of 100,000 binary stars at metallicity Z=0.0001 in a wide range of initial masses and separations. We compared our modelled stars with a sample of 60 CEMP-s stars from the SAGA database of metal-poor stars. For each observed CEMP-s star of the sample we found the modelled star that reproduces best the observed abundances. The result of this comparison is that we are able to reproduce simultaneously the observed abundance of the elements affected by AGB nucleosynthesis (e.g. C, Mg, s-elements) for about 60% of the stars in the sample.