A method for producing a non-oriented electrical steel sheet by subjecting a steel slab having a chemical composition comprising C: not more than 0.0050 mass%, Si: 2.5 to 6.5 mass%, Mn: 0.05 to 2.0 mass%, P: not more than 0.2 mass%, S: not more than 0.005 mass%, Al: not more than 3 mass%, N: not more than 0.005 mass%, Ti: not more than 0.003 mass%, Nb: not more than 0.005 mass%, V: not more than 0.005 mass%, provided that Si, Al and Mn satisfy the following equation: Si − 2 Al − Mn ≥ 0 optionally wherein the steel slab contains at least one group selected from the following groups A-D in addition to the above chemical composition: Group A: one or two selected from Mo and W in an amount of 0.0020 to 0.10 mass% in total, Group B: one or two selected from Sn: 0.005-0.20 mass% and Sb: 0.005-0.20 mass%, Group C: one or two selected from Ca and Mg in an amount of 0.001-0.010 mass% in total, and Group D: one or more selected from Cu: 0.01-0.2 mass%, Ni: 0.05-1 mass% and Cr: 0.01-0.5 mass%, and the residue being Fe and inevitable impurities to hot rolling, hot band annealing, cold rolling, finish annealing and stress relief annealing, wherein the soaking temperature in the hot band annealing falls within the range of 800 to 1100°C, wherein the finish annealing is a continuous annealing of soaking the sheet at a temperature of 700 to 1000°C for 1 to 300 seconds, wherein the stress relief annealing is conducted such that a soaking temperature is 780 to 950°C and a cooling rate from the soaking temperature to 650°C is not more than 10°C/min, and wherein conditions of the finish annealing and stress relief annealing are adjusted such that a yield stress after the finish annealing is not less than 400 MPa, wherein the yield stress is an upper yield point when a JIS No. 5 test specimen is subjected to a tensile test according to JIS Z2241, iron loss W 10/400 in W/kg after the stress relief annealing satisfies the following equation: W 10 / 400 ≤ 10 + 25 t in relation to a sheet thickness t in mm, an average value λ ο-p (bake) of magnetostriction in a rolling direction and magnetostriction in a direction perpendicular to the rolling direction at 400 Hz and 1.0 T after the stress relief annealing is not more than 5.0 × 10 -6, and a ratio (λ ο-p (bake) / λ ο-p (green)) of the above average value λ ο-p (bake) of magnetostriction after the stress relief annealing to an average value λ ο-p (green) of magnetostriction in the rolling direction and magnetostriction in the direction perpendicular to the rolling direction at 400 Hz and 1.0 T before the stress relief annealing is less than 0.8. Group A: one or two selected from Mo and W in an amount of 0.0020 to 0.10 mass% in total, Group B: one or two selected from Sn: 0.005-0.20 mass% and Sb: 0.005-0.20 mass%, Group C: one or two selected from Ca and Mg in an amount of 0.001-0.010 mass% in total, and Group D: one or more selected from Cu: 0.01-0.2 mass%, Ni: 0.05-1 mass% and Cr: 0.01-0.5 mass%, and the residue being Fe and inevitable impurities to hot rolling, hot band annealing, cold rolling, finish annealing and stress relief annealing, wherein the soaking temperature in the hot band annealing falls within the range of 800 to 1100°C, wherein the finish annealing is a continuous annealing of soaking the sheet at a temperature of 700 to 1000°C for 1 to 300 seconds, wherein the stress relief annealing is conducted such that a soaking temperature is 780 to 950°C and a cooling rate from the soaking temperature to 650°C is not more than 10°C/min, and wherein conditions of the finish annealing and stress relief annealing are adjusted such that a yield stress after the finish annealing is not less than 400 MPa, wherein the yield stress is an upper yield point when a JIS No. 5 test specimen is subjected to a tensile test according to JIS Z2241, iron loss W 10/400 in W/kg after the stress relief annealing satisfies the following equation: W 10 / 400 ≤ 10 + 25 t in relation to a sheet thickness t in mm, an average value λ ο-p (bake) of magnetostriction in a rolling direction and magnetostriction in a direction perpendicular to the rolling direction at 400 Hz and 1.0 T after the stress relief annealing is not more than 5.0 × 10 -6, and a ratio (λ ο-p (bake) / λ ο-p (green)) of the above average value λ ο-p (bake) of magnetostriction after the stress relief annealing to an average value λ ο-p (green) of magnetostriction in the rolling direction and magnetostriction in the direction perpendicular to the rolling direction at 400 Hz and 1.0 T before the stress relief annealing is less than 0.8.