This and the following two papers report results of the first comprehensive computer simulation of the behavior of the earth's inner magnetosphere during a substorm-type event. Our computer model self-consistently computes electric fields, currents, and plasma distributions and velocities in the inner-magnetosphere/ionosphere system (L≲10); parallel electric fields and ionospheric neutral winds are not included. In this paper, we derive the basic equations of the model, describe the inputs, and present an overview of results. The first appendix presents derivations of general, useful laws of bounce-averaged gradient, curvature, and E>˜¿B>˜ drifts in a plasma with isotropic pitch angle distributions. A second appendix describes the numerical method used in our computer simulation. The succeeding two papers present analyses of model results and comparisons with data. The model was applied to a substorm-type event that occurred on September 19, 1976. Satellite data (primarily from the Air Force S3-2 satellite) were used extensively both for boundary conditions and for comparisons with model predictions. Other data were also used as input for our time dependent magnetic field and conductivity models. The S3-2 data for the event show some novel features, independent of the simulation. Dawn-dusk electric fields show a general correlation with east-west magnetic field perturbations. Unexpectedly, two of the passes display substantial regions of sunward plasma flow poleward of the main part of the region 1 Birkeland currents. The cross-polar cap potential drops computed from the data represent the first effort at satellite monitoring of this important parameter during various phases of a substorm, and show an important enhancement during the substorm. Numerical results from these first-try simulations are consistent with most of the established features of convection in the inner magnetosphere, such as generally sunward flow, shielding of the potential electric field for L<5, and the tendency for stronger electric fields˜ on the duskside than on the dawnside. In addition, the model reproduces some typical substorm phenomena, such as energy-dependent particle injection with a dawn-dusk asymmetry and establishment of a partial ring current.