Two dimensional models of thermal oxidation of silicon, including those implemented using the SProcess application in the TCAD SenTaurus environment, are analyzed. A number of practically important test structures, which demonstrate the peculiarities of the modeling, are used for the numerical experiments. In the course of the analysis and numerical modeling, the most accurate model is found that closely describes various "thin" phenomena occurring in the course of thermal oxidation of nonplanar silicon surfaces; the model is in close agreement with the experimental data. It is shown that the effect of various nonlinear mechanical phenomena is to be taken into account to provide the adequacy of the modeling. The model is calibrated to provide consistent results and increase the accuracy of modeling.