From the fatigue test of notched specimens of isotropic 70:30- brass, under bending, torsion, and combined stress state of them, a simple criterion for the slip-band crack initiation has been obtained. In spite of the complexity of the triaxial stress state below the notch root, only two stress components, the maximum shearing stress τ_max and the normal stress σ_n acting on a particular slip plane, are responsible for initiating slip-band cracks. Using the averaged stress values over the half-grain-size depth below the notch root, linear sum of them, τ_max + a·σ_n, acts just as the torsional stress in unnotched specimens. At the fatigue limit, therefore, the value for any combined stress state coincides with the torsional one. This relation is more general than the one which has been obtained before for unnotched specimens because of including the case for the unnotched as an extremely shallow notch.