Methods for analysis of texts and separate sentences in a natural language are under discussion. Their main application is to study a written speech with the help of mathematical logic, syntactic rules and the morphology of the modern Russian literary language. Various algorithms for matching predicates and formulas of first order predicate calculus with natural language texts are considered. Also some finite models are matched with parts of text and the text as a whole. The results of this paper may be applied in computer-aided systems of extracting information from natural language texts, in intellectual systems of searching information in the Internet, etc.