Self-ignition within a cylindrical tube that discharges high-pressure hydrogen results in flame formation. Because rectangular tubes are used to visualize fuel-flow dynamics, the influence of the tube cross-section on the self-ignition characteristics is investigated. As experimental investigation of the mechanisms underlying the self-ignition phenomenon in cylindrical tubes is difficult, three-dimensional numerical simulation is employed. Following the bursting of diaphragm by high-pressure hydrogen with a storage pressure of 9.0 MPa and a temperature of 300 K, initial self-ignition occurs at the center of the rectangular tube sidewall. This is because of the mixing of air and hydrogen induced by the bow-shock reflection-generated jet flow and resulting adiabatic shock compression-induced temperature increase. This temperature rise induces a secondary self-ignition at the tube corners. In the cylindrical tube, a solitary ring-shaped self-ignition occurs near the sidewall. The flame evolutions in rectangular and cylindrical tubes reveal similar flame-spreading trends, which indicates similar bow-shock reflection-induced self-ignition mechanisms.