In this paper, a behavioral static model of GaN HEMT is proposed. Different mathematical formulas have been tested to find the best for emulating the static behaviour of a 650V GaN HEMT prototype manufactured by STMicroelectronics. In literature, almost all the proposed formulas did not satisfy the target characteristics. The study of the new mathematical formulas, proposed in this paper, starts from the analysis of the models present in the literature that are rewritten and adapted for this model. Furthermore, these new equations are temperature dependent. The simulated curves of the static characteristics have been compared with those extracted by means of laboratory measurements. The model has been developed exploiting some features of STMicroelectronics models of SiC power MOSFETs.