Barium stars are one of the important probes to understand the origin and evolution of slow neutron-capture process elements in the Galaxy. These are extrinsic stars, where the observed s-process element abundances are believed to have an origin in the now invisible companions that produced these elements at their asymptotic giant branch (AGB) phase of evolution. We have attempted to understand the s-process nucleosynthesis, as well as the physical properties of the companion stars through a detailed comparison of observed elemental abundances of 10 barium stars with the predictions from AGB nucleosynthesis models, FRUITY. For these stars, we have presented estimates of abundances of several elements, C, N, O, Na, Al, α-elements, Fe-peak elements, and neutron-capture elements Rb, Sr, Y, Zr, Ba, La, Ce, Pr, Nd, Sm, and Eu. The abundance estimates are based on high resolution spectral analysis. Observations of Rb in four of these stars have allowed us to put a limit to the mass of the companion AGB stars. Our analysis clearly shows that the former companions responsible for the surface abundance peculiarities of these stars are low-mass AGB stars. Kinematic analysis has shown the stars to be members of Galactic disc population.