To provide a method for producing a low yield ratio and high tougness rectangular steel pipe low in yield ratio, excellent in low temp. toughness and free from the need of a heat treating stage.

A steel stock contg. ≤0.20% C and preferably contg. one or two kinds among 0.40 to 0.90% Mn, 0.005 to 0.040% Nb and 0.005 to 0.050% Ti is subjected to a hot rolling stage in which it is formed into a coil by hot rolling at ≥55% draft in the unrecrystallization temp. region, 730 to 830°C rolling finishing temp. and ≤550°C coiling temp., a pipe making stage by electric resistance welding and a cold rectangle forming stage in which the contraction of the outer circumferential length is regulated to ≤ three times of the sheet thickness to produce the objective low yield ratio and high toughness rectangular steel pipe.