The graduation thesis treats the comparison of two two-dimensional mathematical models and the results produced on debris flow example. The models are known as PCFLOW2D and FLO – 2D and were used for debris flow simulations. In the first part of the diploma work there are teoretical basis of a debris flow, its classification, physical and other important characteristics and features concerning its movement. Basic equations and input parameters of both models (PCFLOW2D and FLO-2D) that were used in calculations are given next. Further on, all data known up to now about the formation, causes and the consequences of the debris flow at the territory of Koseč are resumed. All the projects considering the problems of debris flows at the territory of Koseč that have already been finished are also descibed in this section. By using numerical simulations with one-dimensional domestic model PLAZ1D and two-dimensional comercial model FLO-2D, experts want to prevent or mitigate the damage that another debris flow might cause if it occures. Additionally, the computations on the same landscape have been performed with the domestic two-dimensional model PCFLOW2D. The results of both models FLO-2D and PCFLOW2D are to some extent different although the same input data such as Manning's coefficient, yield strength, viscosity and others have beeen used. The main goal of this diploma work is to answer the questions why it comes to the differences between the two models and how big they are.