The initial oxidation process of a hydrogen terminated Si surface was investigated by molecular orbital calculations using the cluster models representing H-Si(100)-2 x 1 and H-Si(111)-1 x 1. Ab initio calculations using small cluster models revealed that as a Si atom is coordinated by more oxygen atoms, it increases the affinity toward another oxygen. Furthermore, the insertion of up to five oxygen atoms into Si-Si bonds of large models were traced by the semiempirical AM1 method, whose reliability was proven by comparison with ab initio results. The structural relaxation was suggested to be as important as the electronic effect on the stability of oxides, and on the HSi(111)-1 x 1 surface-oxidation was predicted to proceed to the second layer before its completion on the first layer to avoid a large strain which otherwise would be caused. It was also revealed that on the H-Si(100)-2 x 1 surface, the growth of the oxide island and the nucleation of oxide at a distant site have almost the same probabilities. In contrast, the lateral growth of the oxide island is preferred to the formation of an isolated oxide nuclei on the H-Si(111)-1 x 1 surface. These differences derive from the different Si-Si bond topology on each surface.