To produce a rectangular steel tube excellent in brittle fracture resistance in high speed deformation by subjecting a steel having a specified componental compsn. in which each content of S and O is prescribed to cold rectangular tube forming and thereafter executing heating at a specified temp.

A steel contg., by weight, 0.03 to 0.25% C, 0.05 to 0.50% Si, 0.3 to 2.0% Mn, ≤0.1% Al, ≤0.005% S and ≤0.003% O is subjected to cold forming into a rectangular tube. Next, this rectangular steel tube is subjected to heating treatment at ≥600°C. In this way, the rectangular steel tube in which the phenomenon of increasing the percent brittle fracture in the stress- concentrated part does not occur even in high speed deformation and excellent in brittle fracture resistance can be obtd.