System modeling in an object-oriented manner at the initial stage of software development can be considered as a comprehensive knowledge presentation, which enables the developer practice problem domain (instead of code) to reuse and to share responsibilities between system objects at the high enough level of system abstraction. Unified Modeling Language (UML) is an industrial standard for software specification, modeling and software development in object-oriented manner. UML is not a methodology for how to model a system and to develop a software, but just a notational conventions for “drawing” of model elements. And developers have to identify model elements from problem domain based on some guidelines or their own intuition. It can arouse and frequently arise situations, where system model is not adequate to problem domain and has information loss, duplication and discrepancy. The paper offers to use two-hemisphere model driven approach for system modeling at the problem domain level to avoid problems of manual or intuitive system modeling, and illustrates how two-hemisphere model can be translated into software model expressed in UML by using rules for graph transformations. The problem domain of assigning the pupils of the driving school has been adopted for the illustration case study.