Room temperature sorption kinetics is conducted on semi-crystalline ethylene-co-butyl acrylate (EBA) polymer samples filled with different contents of carbon black (CB) in polar (ethanol) or non-polar (toluene) solvents. Equilibrium swelling data obtained by solvent uptake measurements are found to decrease as the CB content increases. This is due to the increase of the crosslink density and tortuosity inside the EBA/CB samples. The preferential area occupied by the solvent molecules in the samples is determined by analyzing the behavior of the wetting coefficient. Higher equilibrium uptake and faster solvent penetration are observed for toluene compared to the case of ethanol. Billmeyer's approach, that is phenomenologically sound and insightful while mathematically straightforward to implement, is applied where the specific parameters of this approach are determined from experiments. Subsequently, the transport mechanisms are discussed using the Peppas-Sahlin and Berens-Hopfenberg relaxation-diffusion models. A significant drop in the tensile properties is observed in the swollen samples compared to their dry counterparts. Furthermore, the sorption data and the mechanical response are found to be well correlated. Additionally, the stress-strain curves of the swollen and dry samples under large deformation are analyzed with the Haward-Thackray model by considering microstructure characteristics (CB content, strain hardening modulus, entanglement, cross-linking degree and polymer-solvent interaction).