The modern engineering design, structures, and especially machines running of new technologies set to engineers the problems that require immediate solution. Therefore, the importance of the method of dimensional analysis as a tool for ordinary engineer is increasing, allows developers to get quick and quite simple solution of even very complex tasks. The method of dimensional analysis is being applied to almost any field of physics and engineering, but it is especially effective at solving problems of mechanics and applied mechanics – hydraulics, fluid mechanics, structural mechanics, etc. Until now the main obstacle to the application of the method of dimensional analysis in its classic form was a multifactorial problem (with many arguments), the solution of which was rather difficult and sometimes impossible. In order to overcome these difficulties, the authors of this study proposed a simple method – application of the combined option avoiding these difficulties. The main result of the study is a simple algorithm which application will make it possible to solve a large class of previously unsolvable problems.