In this article, we examine an allocation issue faced by European Health Union (EHU). Given this situation, we introduce the issue of vaccine selection. The model proposed in this paper helps to implement vaccination optimally using matching theory. By adopting the mechanism presented in this article, this is done more easily and more quickly, so that mortality in society is lower and public satisfaction is increased. This is similar to the issues analyzed in the literature on the design mechanism of non-perishable goods.