This paper discusses the problem of applying Kazimierz Ajdukiewicz’s method of syntactic analysis to incomplete expressions that occur in natural languages. The author defends the claim that it is impossible effectively to apply syntactic analysis to any expressions of natural languages, due to the presence of incomplete expressions. First, the author outlines the basic concepts and describes Ajdukiewicz’s selected views on incomplete expressions, as well as his method of syntactic analysis. Second, using the example of various types of incomplete expressions, the author presents problems that arise when syntactic analysis is applied to expressions of natural languages.