The paper presents current approaches to the analysis and methods of studying the shapes of ancient ceramic vessels. They are based on the developments of G. Birkhoff, A. Shepard, and H. Nordstrom. Most techniques rely on comparing the proportions of the vessel. One of the most widely used programs is the statistical processing of ceramics from the archaeological excavations of V. F. Gening. A. A. Bobrinsky and Yu. B. Tsetlin substantiate the method of studying the natural structure of pottery forms and identifying so-called familiar forms and imitations. The article presents the results of studying vessel shapes using these methods, taking into account the transition time from the Bronze Age to the Early Iron Age of Western Siberia Linevo-1, Om-1 and Mylnikov. The conclusion is made about the similarity of the complexes in the presence of individual features and individual monuments. The possibility of using all existing methods for solving different problems is considered. Keywords: ceramic vessel shapes, approaches and methods for studying ceramic vessels, shape indexes, shape classes according to general proportionality. Domestic and foreign researchers believe that the basis of archaeological classification and typology of ceramic vessels should be their morphological analysis. However, the world community has not yet developed a unified approach to studying the shapes of ancient clay vessels and methods for analyzing the latter. We accept the definition of the term "approach" proposed by Yu.B. Tsetlin: it is "the currently prevailing system of views on the "object" of research, as well as the rules for "ordering" and "interpreting" knowledge about it" [2012, p. 18]. It should be noted that among the publications of the mid-20th and early 21st centuries, only two authors-A. A. Bobrinsky and Yu. B. Tsetlin-are devoted to the analysis of approaches to the study of ceramics, although each researcher involved in the study of ceramics makes his choice in favor of ce ... Read more