Unrestricted Hartree-Fock and density functional theory calculations have been carried out to investigate the detailed kinetics and mechanisms of hydrocarbon thermal cracking. The calculations of the elementary reactions involved in the overall cracking of paraffin molecules agree well with the generally accepted free radical mechanism. The results can be summarized as follows : (I) Initiation cracking, the calculated bond dissociation energy (BDE) for C-C homolytic scission is similar to 95 kcal/mol at the MP2/6-31G* level and similar to 89 kcal/mol at the B3LYP/6-31G* level. No transition states are found in the reactions. (2) II-transfer reaction, the calculated energy barriers (activation energy) are 15-17 kcal/mol at the MP2/6-31G* level and 10-12 kcal/mol at the B3LYP level. The reverse reaction has about the same energy barrier. The calculated transition state structures for both reactions lie in the middle between the reactant and product. (3) Radical decomposition-"beta scission", the activation energy for the radical decomposition is calculated to be 30-33 kcal/mol. The activation energy for the reverse addition reaction is 5 kcal/mol. The optimized transition state structure is product-like for the radical decomposition reaction and reactant-like for the addition reaction.