Hydrogen-elimination reactions on the substrate surface of methane plasma are studied on the basis of an ab initio molecular-orbital method. The activation energy of the reaction of the rate determining step (by MP2/3-21G//HF/3-21G) is much higher than the analogous reaction in silane plasma. In the case of carbon surface reactions, the activation energy becomes larger; as the model cluster size becomes larger, while in the case of silicon surface reactions,the activation energy becomes lower as the model cluster size becomes larger. Thermodynamically, the relative stability of the reactant and the product of the hydrogen elimination reaction on the substrate surface of methane plasma are similar to that of silane plasma. Thus the methane plasma surface reactions are expected to be qualitatively different from silane plasma surface reactions at low substrate temperatures, while they are expected to be similar at high substrate temperatures.