A high power pseudospark switch (40) utilizes a coaxial cylindrical electrode geometry to provide a large number of pseudospark discharge channels (60) in a compact space. The coaxial cylindrical electrode geometry includes a hollow cylindrical anode (52) inside of a larger hollow cylindrical cathode (54). A plurality of radially aligned holes (57, 59) are equally spaced around the perimeter of both the hollow anode and cathode, thereby forming an annular pseudospark discharge (PSD) channel about the coaxial center axis. A plurality of such PSD channels (56, 58) are then stacked along the length of the coaxial cylindrical electrode geometry. A single trigger pulser (48) aligned with the center axis of the cylindrical electrodes provides a way for simultaneously triggering a discharge in each PSD channel. An outer switch housing, divided into two electrically-insulated portions (47, 49) surrounds the coaxial cylindrical electrodes and provides a structural support for the electrodes as well as an electrical contact with the electrodes. A non-conductive seal (43) positioned between the respective housing portions maintains electrical isolation between the respective electrodes, and further allows a specified gas to be maintained within the switch housing at a prescribed pressure, thereby promoting operation of the device on the left side of the Paschen curve.