To improve a cutting yield greatly and secure stable cutting face precision so as to carry out high speed cutting by specifying a line shape and tensile strength of a steel wire consisting of specific constituents such as C, Si, Fe.

This wire contains 0.48-0.90 mass % of C, 0.10-0.50 mass % of Si, 0.15-0.60 mass % of Mn, contents of P, S, Al are limited at most 0.02%, 0.02%, 0.003 mass % individually, an the rest is constructed of Fe and unavoidable impurities. This steel wire is provided with tensile strength MPa satisfying an expression: TS≥-1402×logD+5744, when a final wire diameter is represented by D. The ultra fine steel wire satisfying this required condition is provided with a wire diameter of 15-80 μm, high strength, and high toughness and dutility, so that a cutting yield can be improved while stable cutting face precision can be secured, and cutting can be carried out at high speed. The minimum wire diameter of the steel wire, in which no breakage due to an inclusion is caused, is 15 μm.