Metal-semiconductor field-effect transistors (MESFET's) made of Si, GaAs, and InP have been numerically analyzed in two dimensions using the Cornell University Program for Integrated Devices (CUPID), in order to give physical insight into MESFET operation. Equilibrated electron drift velocity-versus-electric field characteristics and field-dependent anisotropic diffusivities are used in the analysis. Predicted figures of merit, such as cutoff frequency and gate-source capacitance, are compared with experimental results obtained by other authors. Electron transit time, and hence fT, in 0.5- and 1.0-µm-gate Si, GaAs, and InP FET's is shown to be largely unrelated to the value of low-field mobility in these materials at drain voltages in excess of 1 V. The results relate to the choice of materials for devices in both VLSI digital circuits and microwave linear circuits.