Structural change in meat consumption has been the focus of many researchers during the last two decades. In this paper we develop a dynamic linear Almost Ideal Demand System (AIDS) model from a cost function that allows for time varying parameters. This model is consistent with inertia in the parameters of the cost and indirect utility functions. It allows for persistent preferences which may arise from cultural biases, lifestyles, peer pressure, etc. An empirical application is conducted with US meat consumption and price data using a generalized system of flexible least squares, Generalized Flexible Least Squares (GFLS). GFLS allows parameters to evolve slowly over time through incorporating of penalties in fluctuations. Estimated quarterly elasticities were subjected to additional analysis to determine how highly they were related to the Brown and Schrader Cholesterol Index and relative prices. The combined results support that the movements of elasticities over time are related to both.