This paper describes the formal verification of UML model elements using B abstract machines. We study the UML metamodel of class diagrams, collaboration diagrams and state-chart diagrams as well as their well-formedness rules. Each element of UML models which is an instance of a metaclass, is transformed into a B abstract machine. The relationship between abstract machines is organised using the abstract syntax of UML class diagram of the UML metamodel. B specifications are proved by a B prover which generates automatically proof obligations, allowing UML model elements to be verified. The correctness of the UML model elements is ensured by the well-formedness rules which are transformed to B invariants. We illustrate our approach by a simple case study, the printing system.