The relationship between economic and demographic factors and the flow of new students into undergraduate engineering programs was investigated. An empirical analysis was undertaken based on a lagged-supply model developed earlier by Richard Freeman. The analysis involved the replication of the Freeman model over the 1948-1972 period, the extension of the model through 1986, and the forecasting of first-year engineering enrollments up to the year 2000. The model developed in this thesis was able to a accurately mirror the engineering enrollment trends from 1948 to 1986. The economic variables--especially R&D expenditures and starting engineering salaries relative to median income of college graduates--were found to be important factors in the flow of freshmen into engineering. None of the variables relating to demographic trends were found to significantly related to first-year engineering enrollment. The importance of the federal government's role in the engineering labor market through research and development funding is discussed, along with forecasts of possible trends in first-year engineering enrollment.