Concurrent modeling, as an emerging theme in engineering design research, also offers interesting new challenges in applied optimization. However, it is not always clear how best to construct mathematical models that represent such concurrent decision-making. In this paper, a class of engineering design problems, comprising analysis and synthesis tasks, is shown to be a two-player Stackelberg game with synthesis as the leader and analysis as the follower. Situations arising from a reversal of roles of the two tasks are studied and a Pareto model of a Design versus Analysis game is also investigated. Stackelberg games are then viewed in the larger context of concurrent design with design and manufacturing as two players. The potential benefits of such an approach are illustrated in the concurrent design of a stiffened plate structure.