There are two models to calculate friction properties with the DFT, which are constant load model (CLM) and constant interface distance model (CDM). Although the CLM is closer to real friction process, the CDM is more widely used due to its simplicity. In this study, taking typical two-dimension materials as examples, the friction properties were calculated with the CLM and CDM. And the equivalence between the friction properties calculated with the CLM and CDM were veriffed by comparing the potential energy surfaces under the two models. In addition, a link between the friction properties with the CLM and CDM was established by the strategy in which the load under the CDM was deffned as the average load along slid path.