The article is devoted to problems of the shadow economy, reasons for its existence in the modern society. The article discusses the concept of the shadow economy, its types and methods of estimation. It is given a General mathematical interpretation. One developed an agent-based model in Netlogo where we see behavior of the enterprises at change of the tax level and payback period of investment. Emulation experiments’ results are discussed. Also, possible ways that the world society can do to reduce the shadow economy are under discussion in the article.