UML and Simulink are attractive languages for embedded systems design and modeling. An automatic mapping from UML models to Simulink would be an interesting resource in a seamless design flow, allowing designers to use UML asmodeling language for the whole system and at same time to use facilities for code generation based on Simulink. In a previous work, the UML to Simulink translation was prototyped using a Java implementation. In this paper, we present the formal definition of this translation using graph grammars, as well as its automation, which is supported by the AGG system. With the formalization of the metamodels and translation rules, we can guarantee the correctness of the translation. We also illustrate theeffectiveness of our methodology by means of a case study.