In this paper we present an approach to generating instances of metamodels using a Satisfiability Modulo Theories (SMT) solver as a back-end engine. Our goal is to automatically translate a metamodel and its invariants into SMT formulas which can be investigated for satisfiability by an external SMT solver, with each satisfying assignment for SMT formulas interpreted as an instance of the original metamodel. Our automated translation works by interpreting a metamodel as a bounded Attributed Type Graph with Inheritance (ATGI) and then deriving a finite universe of all bounded attribute graphs typed over this bounded ATGI. The graph acts as an intermediate representation which we then translate into SMT formulas. The full translation process, from metamodels to SMT formulas, and then from SMT instances back to metamodel instances, has been successfully automated in our tool, with the results showing the feasibility of this approach.