We extend the classic propositional tableau method in order to compute the models given by the semantics of the Priest’s paraconsistent logic of paradox. Without loss of generality, we assume that the knowledge base is represented through propositional statements in NNF, which leads to use only two rules from the classical propositional tableau calculus for computing the paraconsistent models. We consider multisets to represent branches of the tableau tree and we extend the classical closed branches in order to compute the paradoxical models of formulas of the knowledge base. A sound and complete algorithm is provided.