The objective is to propose an effcient computational strategy for critical plane type approaches dedicated to the fatigue life analysis of structures. The formulation developed consists in determining the shear amplitude in the space of the strain or stress tensors describing the mechanical history in the sense of Tresca. The interest lies in the fact that the critical planes can then be deduced from the Mohrs circles without scanning all the possible planes as usual [1]. For computational effciency, an algorithm in optimal time O(n k) with k << n is also proposed. Even if the mathematical formalism is different from the scanning approach of Bernasconi and Papadopoulos [2], comparisons show that similar results are obtained with a highly reduced computation time in the case of multiaxial loadings. REFERENCES [1] B. Agard, L. Giraud, F. Fauvin, J.-C. Roux, P. Monnet and E. Feulvarch, Fast compu- tation of critical planes for fatigue life analysis of metals, Comptes Rendus Mécanique, https://doi.org/10.5802/crmeca.139. [2] A. Bernasconi, I.V. Papadopoulos, Effciency of algorithms for shear stress amplitude cal- culation in critical plane class fatigue criteria, Computational Materials Science, 34 (2005) 355-368.