Electron-beam-induced current (EBIC) measurements can be used in order to investigate microscopic electrical properties of semiconductor materials and devices. However, for the estimation of material parameters and the unequivocal interpretation of EBIC micrographs, very often additional simulations are necessary. Up to now, these simulations have been carried out mostly using analytical models based on some restrictive simplifications. These models can only be used for simple specimen structures of high symmetry or for specimens that can be definitely separated into such simple structures. These models are not well suited to the simulation of electron beam currents in small devices such as MESFETs (metal-semiconductor field-effect transistors). Thus, we have used the more adaptable finite difference method for two-dimensional numerical simulations of electron-beam-induced gate currents in these devices. In this first part of the paper, the model and tools used are presented.