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Transesterification of alkyl esters plays an important role in biodiesel production, and a critical substance in this mechanism is triacylglycerol. A molecular modeling technique is used in this study to determine the geometrical parmeters of triacylglycerol via semi-empirical AM1, PM3 and ab initio HF/6-31G with the GaussView 03W and GAUSSAIN 03W pieces of software. The results obtained from these three models showed that the geometrical parameters of the triacylglycerol molecules are in the same range. Hence, these molecular models can be used in the simulation of the transesterification mechanism. There are six possible mechanisms for the biodiesel transesterifications. Each type of mechanism contains six reaction steps. Using the B3LYP/6-31G//PM3 method, the transesterification mechanism was simulated to determine the best possible pathway.