We propose an approach to verify UML model elements based on the transformation of the UML meta-model into B formal specifications. The UML meta-model is described as a combination of graphical notations, natural and formal languages. The semantics of UML elements is expressed by well-formedness rules in the UML meta-model. Their correctness is ensured by the proof of the B specifications. The approach is illustrated by a simple case study: the printing system.