Most structural components have notches, or geometric transition details such as holes and corners which are required to assemble and/or to operate them. These notches locally increase the nominal stresses that would act in their location, if they were not there. Stress concentration effects are very important in many failure mechanisms, such as fatigue crack initiation. However, the usual constant radius notch tip roots, used in most structural members to alleviate their stress concentration effects, do not minimize them. In fact, natural structural members, such as tree branches, after many million years of evolution have learned to use variable tip radii instead of the fixed radius typical of engineering notches. This problem has been recognized for a long time, but variable radii notches optimized to minimize their deleterious influence on fatigue strength still are not widely used in mechanical design. The usual practice is to specify notches with as large as possible constant radius roots, since they can be easily fabricated in traditional machine tools. However, notches with properly specified variable radius can have much lower stress concentration factors than those obtainable by fixed notch root radii. Therefore, such improved notches can be a good design option to augment fatigue lives without significantly affecting structural components global dimensions and weight. Moreover, these improved notches are certainly more useful than ever, as nowadays they can be manufactured in many structural components, due to the wide availability of CNC machine tools. This dissertation aims to quantify the stress concentration improvements achievable by traditional variable radii notches receipts, and presents a numerical routine, developed in ANSYS APDL to optimize notch shapes of mechanical components such as shoulders in plates subjected to tension or bending, plates with a hole subjected to a biaxial stress field, and standard ASTM fatigue test specimens.