Display omitted ► Continuum mechanics based approximation is too often unsatisfactory for real material’s problems. ► Deterministic analyses often produce inconclusive, or conflicting, in estimating the fatigue life of a component. ► Cracks are described better with fractal mathematics than with Euclidean mathematics. ► Possibility of the applications of probabilistic and fractal fracture mechanics is predicted. Continuum mechanics-based approximation is too often unsatisfactory for solution of real material problems especially in experimental as well as computational fatigue applications. Various methods of classical-deterministic analyses often produce inconclusive or conflicting estimates of the fatigue life of a component. In addition, the classical Griffith–Irwin–Orowan concept that assumed the phenomena based on homeomorphism mathematics cannot be developed any closer to the experimental results anymore. It has already reached its saturation point. This note discusses the fundamental reasons of the limitations of classical fracture mechanics and subsequently predicts alternatives. Application of classical fracture mechanics to engineering problems is discussed along with possible alternatives employing probabilistic and fractal fracture mechanics in materials engineering.