Abstract: Methane may physically be absorbed on shale in a supercritical state within shale reservoirs. Based on these characteristics, research has been conducted for isothermal absorption models of supercritical methane in shale. Excess adsorption is introduced to correct conventional adsorption models, such as Langmuir, Freundlich, Expended-Langmuir, Langmuir-Freundlich, Toth, B-BET, T-BET, D-R and D-A. Thus, conventional adsorption models are expanded into supercritical adsorption models. In addition, relative error is used to assess fitting results for isothermal adsorption of supercritical methane on shale before and after correction for those adsorption models. By analyzing the physical significance of fitting parameters in these models, it is possible to investigate features and mechanisms of adsorption in shale. There are certain differences in absorption mechanisms reflected by fitting the parameters of the absorption models.In particular, multi-molecular layers BET models (B-BET and T-BET) and Expand-Langmuir model have no physical significance for some shale samples. Accordingly, these models can no longer be used to determine features of supercritical methane adsorption. Furthermore, fitting parameters generated through Langmuir model and D-A model can accurately reflect supercritical methane adsorption characteristics. Comparison of the fitting results shows that the corrected adsorption model fits better than the originalone. The corrected Freundlich model fits badly, while the corrected Toth and D-R models display better performances than the corrected Langmuir model. But the overall fitting performances are not satisfactory. The corrected Langmuir-Freundlich model and D-A model have better performance in terms of fit. Research results show that fitting parameters determined by using the corrected D-A model are suitable for fitting the supercritical isothermal adsorption of methane in shale. Accordingly, the corrected D-A model can be seen as a desirable model for representation of supercritical methane adsorption characteristics in shale.