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The electric field distribution along the interface of a solid insulator-vacuum (or gas) is analyzed for different solid insulator-electrode configurations with and without the presence of surface charges using the charge simulation technique. The tangential component of the electric field at the solid insulator-electrodevacuum (or gas) triple junction is found to be reduced in cases where the contact electrode extends into the solid insulator and where the solid insulator is placed in a recessed electrode. The reduction in the field increases with increasing the penetration length of the metal insert and the depth of the recess in the electrode. The results give a theoretical justification for the previously observed higher flashover values for insulators with metal inserts and for those placed in recessed electrodes.