The present invention provides steel plate or steel pipe with small occurrence of the Bauschinger effect and methods of production of the same, particularly steel pipe used for steel pipe for oil wells or line pipe with a small drop in the compression strength in the circumferential direction due to the Bauschinger effect when expanded and methods of production of the same, that is steel plate or steel pipe with small occurrence of the Bauschinger effect characterized by having a dual-phase structure substantially comprising a ferrite structure and fine martensite which is dispersed in the ferrite structure. Further, this steel plate or steel pipe contains, by mass %, C: 0.03 to 0.30%, Si: 0.01 to 0.8%, Mn: 0.3 to 2.5%, P: 0.03% or less, S: 0.01% or less, Al: 0.001 to 0.01%, and N: 0.01% or less and a balance of iron and unavoidable impurities.