This paper relates social mobility and social stratification to the structure of higher education. We develop an intergenerational model which shows that a two-tier higher education characterised by a division between elite and standard universities can be a key factor in generating permanent social stratification, social immobility and self-reproduction of the ‘elite’. In our approach, low mobility at the top is essentially explained by the differences in quality and in selection between elite and standard universities. A key result is that the wider the quality gap and the difference in per-student expenditures between elite and standard universities, the less social mobility. This is because a larger quality gap reinforces the weight of family backgrounds at the expense of personal ability. Our simulations show that this impact can be large. These findings provide theoretical bases for the differences in social mobility at the top observed between advanced countries.