A direct relation where fatigue life $N_f$ can be determined as a function of macroscopic normal and shear stress amplitudes ${\sigma }_a$ and ${\tau }_a$ is established. Using the Carpinteri & Spagnoli (C&S) criterion as a survey tool, elliptical-level curves in the ${\sigma }_a\times {\tau }_a$ domain were revealed and further generalized, providing means to determine $N_f$ for any given $\left({\sigma }_a,{\tau }_a\right)$ combination. Predictions obtained through the elliptical curve method (E) were compared with experimental observations, as well as with predictions obtained from adapted versions of popular fatigue criteria, namely, Findley (F), Matake (M), McDiarmid (McD), Susmel & Lazzarin (S&L), C&S, and Papadopoulos (P). The proposed model delivered predictions in fair agreement with experimental observations, and its predictive capability was seen to be the best among all the considered criteria. Finally, a slight bias toward conservativeness was attenuated with the introduction of an adjusting parameter, further improving the predictive capability of the model.