There exist various models for Microwave MESFET equivalent circuit representations. These models use different mathematical models to describe the same MESFET and give similar results. However, there are some differences in the results when compared to the experimental measurements. In this thesis, various theoretical models are applied to the same MESFET and comparison made with measured data. It is shown that some models worked better on some parameters of the MESFET, while the others were more effective on other parameters. Altogether eight models were examined and data optimized to fit these theoretical models. In using optimization algorithms MATLAB FMINSEARCH and GENETIC ALGORITHM CODE were used alternatively to solve the initial value problem.