In the production of a non-oriented electrical steel sheet by subjecting a steel slab having a certain component composition to a hot rolling, a hot-band annealing, a cold rolling and a finish annealing, the conditions of the finish annealing are controlled such that a yield stress of the steel sheet after the finish annealing is not less than 480 MPa. Also, when a motor core is produced by using the above steel sheet, there can be provided a non-oriented electrical steel sheet capable of producing a rotor core and a stator core as the same raw material where the stator core is subjected to a stress relief annealing at a soaking temperature of 780 to 950° C. in an atmosphere having a nitrogen content of not more than 30 vol % and a dew point of not higher than −20° C., while a motor core is produced with such a steel sheet.