A notch in a structural component can easily provoke the initiation and growth of a surface crack because of stress concentration. The stress field for this component can be rather different from that found out in an unnotched component with an identical surface flaw, and fatigue life may heavily be affected by such a geometric discontinuity. In the present paper, the influence of a circular-arc circumferential notch in a round bar is analysed. Firstly, the Stress Concentration Factor (SCF) related to tension loading is determined. Then, an elliptical-arc external surface flaw is assumed to exist at the notch root, and the Stress Intensity Factor (SIF) along the crack front is computed through a finite element analysis for both tension and bending, by varying the stress concentration factor from 1.0 (smooth bar) to about 3.0 (small notch radius). The effect of the stress concentration on the SIF values is discussed for the considered crack configurations. Finally, the surface crack propagation under cyclic loading is examined through a numerical procedure which takes into account the computed SIF values.