A computer model of fast-acting electromagnetic actuators has been developed which accounts for magnetic saturation, flux leakage, eddy currents, squeeze-film fluid damping with inertia effects, and the dynamic coupling of the actuator state variables. The governing equations for each actuator subsystem are developed and solved as a system of nonlinear ordinary differential equations using Gear method. This model maintains the simplicity of a lumped-parameter approach and relies on a minimum of empiricism. The model was verified at various levels of system complexity. Predicted steady-state magnet forces showed very good agreement with experimental results over a range of magnetomotive forces from 50 to 900 amp-turns and with gap lengths from 25 to 1000 microns. In addition, the model predicts transient actuator behavior and the proper dynamic coupling between the electrical, magnetic, mechanical and fluid subsystems. Experimental and predicted results for armature motion in air, hexadecane and glycerine show excellent trend-wise agreement and demonstrate the necessity of the inclusion of fluid inertia in the squeeze-film analysis.