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This paper deals with the investigation of current interruption in the hollow-cathode discharge as applied to the electrode configuration of pseudospark switch. The phenomenon of interruption manifests itself at currents of several kiloamperes or higher and at a low gas pressure. It is demonstrated that the region of the hollow cathode is able to pass a high current density. The region that is responsible for the current interruption is the main gap of the switch, i.e., the positive column of discharge. The theoretical model of the positive column is proposed. The model implies that the gas ionization in the column is provided by the fast electrons which are accelerated in a double electric layer at the exit of cathode cavity. The estimates with a usage of the model are in agreement with the experimental data.