A generalized fatigue criterion for materials under multiaxial random loadings is presented. The criterion is based on the assumption that shear and normal strain on the expected fracture planeshear strain in one direction on this plane is considereddetermine the fracture plane. It has been shown that the well known fatigue criteria of maximum normal strain, maximum shear strain and the criterion of maximum shear and normal strains on the critical shear plane result from the newly formulated criterion.Mat.-wiss. u. Werkstofftech. 22, 203-210 (1991) 0933-5137/91/0606-0203$3.50 + .25/0 203 0 VCH Verlagsgesellschaft mbH, D-6940 Weinheim, 1991