The article reviews the principal existing approaches to estimating the needed number of Masters students and presents data on the first attempts at introducing Masters programs in Russia. The authors discuss specifics of Masters programs in countries with a considerable experience in two'stage education programs, including how to determine the share of Masters students in the student population. Using data on the dynamics of the number and age distribution of scientists, project engineers, and teachers at technological universities, the authors forecast the demand for graduates with Masters degrees in technology in the near future. They formulate the principal conditions for a university to open Masters programs. Calculations comparing the costs of Masters and Specialist training are presented.