The world depends on petroleum for everything from the plastics that contain our food to the natural gas that heats our homes to the gasoline that feed our cars' engines. With rising prices of petroleum reflecting demand for this finite resource, attention has been turned to alternative sources of energy. Biodiesel, which exhibits many of the same properties as conventional diesel but is derived from biological sources, is an attractive alternative. Fats and oils are converted to biodiesel, fatty acid methyl esters (FAMEs), by transesterification. FAMES are subsequently thermally cracked to form more lightweight transportation fuels such as natural gas, kerosene, and possibly gasoline. We aim to further understand the thermal cracking procedure, at an atomic level, in hopes that this may aid in future engineering of viable fuels. We will present our study on the effective computational modeling of bond dissociations in the FAMEs methyl linoleate and methyl oleate, which are the most common biodiesel products of soybeans and rapeseeds (also known as canola seeds). We have employed quantum chemical methods, including the density functionals B3LYP, M06-2X, and B97D; the wave function-based MP2; and the composite CBS-QB3 method. Bond dissociation in a 44-reaction database set for which experimental energies are known is used to evaluate methods. We find that the M06-2X/6-31+G(d,p) model chemistry provides results comparable to the composite CBS-QB3 method at a much reduced cost. Last, data are compiled for possible bond dissociations in FAMEs methyl oleate and methyl linoleate.