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Mathematical Remodeling is aimed at transforming mathematical or simulation models of one or different classes (or subsystems forming a studied system) into a model of one predefined unified class. Depending on the goals and specific applications, different interpretations of remodeling are possible. Theoretical model constructed based on its physical meaning, can be quite complicated and is not suitable for further analysis. In this case, an array of input and output training data (which could not be obtained in real conditions) can be generated using the software implementation of the model. Using these obtained values and according to Remodeling concept it is necessary to determine a new model of a given structure with the required accuracy, which can approximate the original model in the best way. The paper presents examples of applying Mathematical Remodeling concept to constructing a dynamic system with a variable structure. Such systems are used to simulate an inertial torque transformer, which is a part of a stepless car transmission. Another example of this approach is the method of estimating freeway section capacity. Feedforward neural networks are used as remodeling classes in both cases. The introduced applications of Mathematical Remodeling approach are in the basis of constructing intelligent transportation systems.