Our experiments demonstrate that PS is completely soluble in methyl esters over the range of molecular weights studied (80,000-980,000 Da). LDPE is also soluble in biodiesel, but only at elevated temperatures and at low polymer molecular weight (below 6500 Da). The dissolution kinetics of PS and LDPE in methyl esters was monitored by gravimetric methods and FTIR imaging. Dissolution rates of the two polymers as a function of polymer molecular weight and temperature were extracted from the experiments. From the data, parameters such as activation energies and scaling indices (of dissolution rate vs. polymer MW) were estimated. Other properties of the PS (LDPE)/biodiesel solution such as shear viscosity and particle size in solution were also characterized. Together, the dissolution and the shear viscosity experiments provided conditions in which these solutions could be used as fuel in engines. To complement the experimental investigations, molecular dynamics simulations were employed to construct models of methyl esters, and parameters such as cohesive energy densities and solubility parameters were calculated. These properties were used to predict thermodynamic polymer/solvent interaction parameters and based on these calculations, phase diagrams were constructed. The modeling work also provides a predictive toolbox to design biodiesels with different compositions (e.g., mixed solvents, and additivies) that will dissolve other common plastics.