Last decades the public debt increased continuously in all countries of European Union. At present, in many countries this dangerous growth is seriously affecting the general process of economic development. Although in a number of countries the public debt is today larger than 60% of GDP, as the imposed limit by Maastricht Treaty, the problem of its sustainability is varying from country to country. Following old and recent published studies in matter of public debt sustainability, one objective of our study is to analyse the existence of a convergence or a divergence process both at the level of the whole EU and within the two major groups of countries (EU14 – old members of EU, after Brexit, and respectively EU11 – new eastern members adhered to EU after 2000). Other objective is to build a model to simulate the long term dynamics of the public debt as a function of standard variables (such as GDP growth, interest rate, budgetary deficit, etc.). Moreover, by using recent data from Eurostat, IMF, and World Bank, we try to estimate few essential parameters in order to control the public debt sustainability in each country of EU. Finally, countries are grouped in a number of classes for which certain policy measures could be evaluated.