In the present thesis, we reported the use of molecular dynamics (MD) simulation to calculate the self-diffusion coefficients of a hydrophobic drug molecule in a series of micelle-forming PEO-b-PCL block copolymers with different structures and PCL block lengths in the presence of water molecules. MD analysis techniques like velocity auto-correlation functions, and squared displacement values along x, y and z axis provided useful atomistic details to understand the molecular origin of the diffusivity observed for drug molecules. Based on the evidence of reported work, intermolecular specific interactions between drug and different blocks of block copolymers all play important roles in the self-diffusion of drug molecule (CuB) in block copolymers. Additionally, water concentration, polymer swelling and wriggling motion of polymer chains affect the diffusivity of water molecules. The computed radius of gyration (Rg) of the PCL block confirmed that the PCL block tends to exhibit a higher degree of swelling than the PEO block. The understanding of relative contributions of the inter molecular interactions between drug and polymer can help us to customize the performance of drug carriers by engineering the structure of block copolymers to achieve a desired drug self-diffusion.