The new strain-concentration factor (SNCF), defined under the triaxial stress state at the net section, is studied for circumferentially notched cylindrical bars under static tension. The elastic SNCF increases as the net-to-gross diameter ratio do /Do increases and reaches a maximum at do /Do 0.7. Beyond this value of do /Do it rapidly decreases to unity with do /Do. The elastic SNCF of the extremely deep notch of do /Do = 0.2 is almost equal to that of the shallow notch of do /Do=0.95. Nevertheless, the new SNCF of the shallow notch sharply increases with plastic deformation at the notch root, while the new SNCF of do /Do= 0.2 increases only slightly. The new SNCF of the deep notch of do /Do = 0.6 also increases with plastic deformation and reaches a peak value. This peak value is nearly equal to or slightly less than that of the shallow notch and hence the plastic SNCF of shallow notches cannot be neglected. The variations in the new SNCF with P/PY, the ratio of tensile load to that at yielding