We numerically simulated the current density distribution in electrically nonlinear varistor material containing geometrically simple inclusion defects. Nonconductive spheres and disks, which resemble inclusion shapes observed in chemically prepared varistor material, were investigated. Current densities near perfectly conductive spheres and rods were also computed to gain insight into observed electrical degradation phenomena. These defects were assumed to be much larger than the characteristic size of the zinc oxide (ZnO) grain structure, and our computational method treated the varistor material as electrically isotropic. Results showed strong, localized concentrations of current with either perfectly conductive or nonconductive inclusions, and a dependence on the density of the conductive defects. The small spatial extent of strong current intensification may help to explain the stepwise electrical degradation we have observed when a failing ZnO varistor is subjected to high-power electrical pulses.