The accuracy of fitting the rheological model to the properties of actual drilling fluid minimises the errors of the calculated technological parameters applied while drilling oil wells. This article presents the methodology of selecting the optimum drilling fluid rheological model. Apart from classical rheological models, i.e., the Newtonian, Bingham Plastic, Casson, Ostwald de Waele and Herschel−Bulkley models, it has been proposed to consider the Vom Berg and Hahn-Eyring models, which have not been applied to describe drilling fluids so far. In the process of determining rheological parameters for the Bingham Plastic, Casson, Ostwald de Waele and Newtonian models, it is proposed to use a linear regression method. In the case of the Herschel−Bulkley, Vom Berg and Hahn-Eyring models, it is suggested to use a non-linear regression method. Based on theoretical considerations and mathematical relations developed in the Department of Drilling and Geoengineering, Drilling, Oil and Gas Faculty, at AGH University of Science and Technology, an original computer program called Rheosolution was developed, which enables automation of the process of determining the optimum drilling fluid rheological model. Some examples show the practical application of the method of selecting the optimum drilling fluid rheological model. Taking into account data from actual measurements of drilling fluid properties, it has been proven that the Vom Berg and Hahn-Eyring rheological models are best fitted to the description of drilling fluid rheological parameters.