In spite of many multiaxial fatigue life prediction methods proposed over decades of research, no universally accepted approach yet exists. A multiaxial fatigue damage model developed for approximately proportional random amplitude loading is proposed in this study. A normal strain based analysis incorporating the multiaxial state of stress is conducted along a critical orientation assuming a constant strain ratio. The dominant deformation direction is chosen to be the critical orientation which is selected with the help of a principal strain histogram generated from the given multiaxial loading history. The uniaxial cyclic stress-strain curve is modified for the biaxial state of stress present along the critical orientation for the plane stress conditions. Modified versions of Morrow's and of Smith, Watson, and Topper's (SWT) mean-stress models are used to incorporate mean stresses. A maximum shear strain based analysis is, in addition, conducted to check for the shear dominant fatigue crack growth possibility along the critical direction. The most damaging maximum shear strain is chosen after analyzing the in-plane and the two out-of-plane shear strains. The minimum of the two life values obtained from SWT model and the shear strain model is compared with the life estimated by the proposed model with the modified Morrow's mean stress model. The former is essentially the life predicted by Socie. The results of the proposed model, as reduced to the uniaxial case, are also compared with the experimental data obtained by conducting one-channel random amplitude loading history experiments. / Master of Science