Breakdown voltages of gases in parallel-plate geometries are well represented by Paschen's law, whose scaling parameter is pd (gas pressure x electrode separation). In nonplanar geometries, Paschen's law is not directly applicable due to the ambiguity in the distance between the electrodes and distortion of the electric field. A Monte Carlo computer model is used to investigate breakdown characteristics in nonplanar geometries and hollow cathode pseudospark switches in particular. The model tracks the trajectories of both electrons and ions, including ionizing collisions in the gas phase by electrons and ions, and secondary electron emission by ions on surfaces. It is found that under typical operating conditions in helium (0.1 to a few Torr, voltages of tens of kV, effective electrode separation of a few mm), approximately two-thirds of ionizing collisions are attributable to ion impact, of which half are due to ion impact in the gas phase.