Econophysics is an interdisciplinary science that applies methods and theories developed in physics for solving problems in the economy. Catastrophe theory is a theory that is derived from the topology, which is part of mathematical science that studies the properties of surfaces in several dimensions. The theory is a branch of bifurcation theory that is used in the study of dynamic systems, it is also a special case of a more general theory of singularity which can be found in geometry. This paper analyzes the catastrophe theory as a part of econophysics, but I did not focus only on the examples that use economic theory and files that are collected in the field of the economy. Given that many sciences are involved in econophysics, and in many ways contribute to econophysics, the content of my paper I imagined as a general introduction and familiarization with the econophysics, and processing a catastrophe theory, starting from the simplest through to more complex models.