The glass ceiling effect has been defined in a recent US Federal Commission report as "the unseen, yet unbreakable barrier that keeps minorities and women from rising to the upper rungs of the corporate ladder, regardless of their qualifications or achievements". It is well documented that many societies and organizations exhibit a glass ceiling. In this paper we formally define and study the glass ceiling effect in social networks and propose a natural mathematical model, called the biased preferential attachment model, that par- tially explains the causes of the glass ceiling effect. This model consists of a network composed of two types of ver- tices, representing two sub-populations, and accommodates three well known social phenomena: (i) the "rich get richer" mechanism, (ii) a minority-majority partition, and (iii) ho- mophily. We prove that our model exhibits a strong mo- ment glass ceiling effect and that all three conditions are necessary, i.e., removing any one of them will prevent the appearance of a glass ceiling effect. Additionally, we present empirical evidence taken from a mentor-student network of researchers (derived from the DBLP database) that exhibits both a glass ceiling effect and the above three phenomena.