The aim of this paper is to contribute, in the theoretical and empirical sense, to better understanding the challenges of the EU welfare regimes and how particular regimes react on them. Despite significant differences among the EU welfare regimes, it is real to expect that they will converge because of the common challenges confronting them. In this paper, using the model of sigma and beta convergence, we are trying to predict the possible direction of convergence in the sense that Europe will go toward to more or less generosity or in other words it will converge downward or upward. The downward convergence means the strengthen competition among existing welfare regimes, in order to maintain and/or attract capital, that could reduce the social spending generosity. On the other hand, the upward convergence above involves the strengthening of coordination among existing welfare regimes according to the values of solidarity and social justice, which characterise not only the most developed EU countries but also the supranational European social model. .