High-voltage power transformers incorporate large quantities of insulation which is easily contaminated, and the dielectric strength is, in consequence, uncertain. This paper reports the results of electric-strength tests on transformer oil, alone and in combination with solid insulation, under various conditions. It is concluded that a major factor determining the maximum local oil stress at failure is the volume of oil under the highest stress, and that, from a knowledge of the failure-stress/volume characteristic for oil in uniform fields, the maximum local oil stress at failure for nonuniform fields can be predicted.