The paper presents the method of structural numbers (MSN), which is a relatively new approach to the analysis of a class of lumped mechanical vibration systems. The method, first published two decades ago , is commonly used in the analysis and synthesis of electrical systems. Ten years later the MSN was also applied to the case of mechanical systems . In recent years the MSN has been substantially developed and also, due to rapid progress in the fields of modification analysis, sensitivity analysis, synthesis and optimization, new areas of application of MSN have been revealed. Therefore, it seems reasonable to present the method briefly. It enables a full automatization of the process of finding trees of mechanical system graphs and, therefore, it constitutes a valuable complement to topological methods. An example of MSN application is given in the paper.