The local strains obtained from the best-known analytical approximations, namely, Neuber's rule, equivalent strain energy density method, and linear rule, were compared with those resulting from finite element analysis. It was found that apart from Neuber's rule with the elastic stress concentration factor, all the aforementioned analytical methods underestimate the local strains for all notch root radius, strain amplitude levels, at room temperature and 550 °C. Neuber's rule withslightly overestimates the maximum strains for lower notch root radius, namely, 1.25 mm, at high temperature. Based on the analytically and numerically obtained notch root strains, the fatigue lives were estimated using the Coffin–Manson–Basquin equation. Besides, a numerical assessment of fatigue lives was made based on Brown–Miller and maximum shear strain multi-axial fatigue life criteria. It was found that all these methods provide inaccurate fatigue life results for all notch root radius, strain amplitude level, and under both temperatures conditions. Therefore, a new method was suggested, for which only the applied strain amplitude is needed to calculate the fatigue life of notched components. It was revealed that the suggested method provides a good fatigue life prediction at a higher temperature loading state.