Polymers are the most commonly used packaging materials for nutrition and consumer products. The ever-growing concern over pollution and potential environmental contamination generated from single-use packaging materials has raised safety questions. Polymers used in these materials often contain impurities, including unreacted monomers and small oligomers. The characterization of transport properties, including diffusion and leaching of these molecules, is largely hampered by the long timescales involved in shelf life experiments. In this work, we employ atomistic molecular simulation techniques to explore the main mechanisms involved in the bulk and interfacial transport of monomer molecules from three polymers commonly employed as packaging materials: polyamide-6, polycarbonate, and poly(methyl methacrylate). Our simulations showed that both hopping and continuous diffusion play important roles in inbound monomer diffusion and that solvent-polymer compatibility significantly affects monomer leaching. These results provide rationalization for monomer leaching in model food formulations as well as bulky industry-relevant molecules. Through this molecular-scale characterization, we offer insights to aid in the design of polymer/consumer product interfaces with reduced risk of contamination and longer shelf life.