The access to Greek tertiary education, and especially to the university medical sector, and the relevant selection processes are influenced by socially determined inequalities. Given that all tertiary education access systems are centralized and centrally organized, research was carried out to investigate to what extent the reformative interventions make the selection process more or less competitive as this results in the advantage (according to priority) of those already privileged due to their social origin. The analysis of the official data of the National Statistics Service of Greece for the period 1984-1998 shows that the father’s profession is an important differentiation factor for relative access possibilities to university medical education and that the respective access inequalities are increasing over time.