High-voltage bushings have exhibited vulnerability during past earthquakes. The good performance of bushings mounted on a rigid base observed during shake table testing does not correlate well with their performance in the field. It is suspected that the seismic performance of high-voltage bushings is improved when mounted on a rigid base, as opposed to when mounted on more flexible cover plates of transformers. In this first of two companion papers, the seismic response of bushings was investigated numerically for various mounting conditions. The addition of flexural stiffeners on the transformer cover plates was explored as a means to stiffen the base of the bushings and mitigate their seismic vulnerability. Linear dynamic analyses conducted on four transformer-bushing system models showed that the simple approach of stiffening the cover plates of transformers is beneficial to the seismic response of high-voltage bushings.