The construction and analysis of the interpretation functions of the models of unsteady dynamics of new generation an underwater vehicle (UV) based on the modern theory of disasters are considered. The formal apparatus of conceptual solutions and principles of constructing interpretation functions is implemented in a non-stationary dynamic environment within the framework of the principle of competition. The procedures of the interpretation functions are based on the use of various interaction models depending on the level of acting disturbances. The uncertainty and incompleteness of the initial information on the dynamics of the interaction of underwater vehicles in a non-stationary environment determined the approach to constructing interpretation functions when constructing a mathematical description of the problems of non-stationary dynamics of underwater vehicles based on the concept of soft computing and the identification of "hidden" knowledge. The developed models and algorithms for interpreting unsteady dynamics of submarines are implemented in the functional block for modeling a multifunctional software complex for dynamic visualization of unsteady dynamics of underwater vehicles in emergency computing mode Urgent Computing.