In this paper, we consider a method of omputing minimal models in circumscription using integer programming in propositional logic and first-order logic with domain closure axioms and unique name axioms. This kind of treatment is very important since this enable to apply various technique developed in operations research to nonmonotonic reasoning. Nerode et al. are the first to propose a method of computing circumscription using integer programming. They claimed their method was correct for circumscription with fixed predicate, but we show that their method does not correctly reflect their claim. We show a correct method of computing all the minimal models not only with fixed predicates but also with varied predicates and we extend our method to compute prioritized circumscription as well.