Triacylglycerides (TAGs) and their related fatty acids (FAs) are abundant in biomass (vegetal oils and animal fats). Here, we studied by theoretical calculations the most representative FAs and their chemical reactions under hydrogen atmosphere to produce O-free hydrocarbon molecules. In general, the Delta H-r(0) and Delta G(r)(0) do not vary due to the size of the molecule. Selected TAGs were also studied by theoretical calculations. Similar as FAs, the overall reaction energies do not depend on the size of the molecules. Possible reaction networks for the hydrogenation and hydrogenolysis processes are proposed for such biomolecules under hydrogen environments. We also studied the profiles of the enthalpy and Gibbs energy of reaction for TAGs at typical operating conditions of temperature or pressure. This self-consistent study is willing to contribute for a better understanding of the reactions of the biomass that take place under hydrogen atmosphere.