Introduction Cyclic fatigue of fiber composite laminates has been an important technical issue ever since composites were introduced to engineering applications decades ago. The ability to accurately predict the long-term fatigue strength and life of a composite laminate structure subjected to multiaxial loading is critically needed. It is essential in the design@ performance evaluation and reliability assessment of composite structures in service conditions. It is recognized that the development of an accurate fatigue life prediction capability requires clear understanding of cyclic deformation and associated damage evolution in the composite material and the establishment of a quantitative@ mechanics-based fatigue failure theory@ involving both microscopic material parameters@ and macroscopic lamination and structural variables as well as external loading modes. The fatigue life prediction problem for a composite laminate is obviously complicated since many issues at different scales are involved. These may include identification of various failure modes@ evaluation of damage evolution and associated property degradation@ establishment of local multiaxial failure criteria at the ply level@ accurate determination of ply deformation and stresses@ and investigation of cyclic loading effects on the composite damage and failure. It becomes obvious that the aforementioned complexities are generally difficult to address in a quantitative manner@ since they require in-depth knowledge of composite material constitutive equations with evolving microstructural changes@ heterogeneous composite microstructure@ continuum material damage mechanics theory@ unknown fatigue failure modes and associated strength criteria@ and a suitable life prediction methodology for the composite laminates subjected to complex multiaxial loading. Extensive studies on cyclic fatigue of fiber-reinforced polymer-matrix composites have been reported in the literature. For example@ Hashin and Rotem[l] and Awerbuch and Hashin[2] have given a large amount of fatigue test data on cyclic behavior of glass/epoxy and carbon/epoxy composites. Empirical and semi-empirical methods have been used to interpret the fatigue test data. Analytical attempts@ such as the one proposed by Hashin [3] on fatigue of unidirectional composites@ have also been introduced to rationalize the complex phenomena of cyclic fatigue failure in multilayer composite laminates@ but only have limited success. Owing to the importance of the fatigue issues in the long-term composite structural safety and performance@ many studies have been and are being conducted. However@ the development of a suitable fatigue life prediction methodology@ based on physically observed failure modes with rigorous fatigue mechanics formulation@ remains to be accomplished. In next section@ a brief review of the literature is made to assess the current status of the subject. The objectives and the scope of work in this investigation are defined in Section 3. Based on the fundamental fatigue failure modes and local failure criteria obtained in several related studies@ a physical mechanism based fatigue life formulation is developed in Section 4 for fiber composite laminates under general loading. In Section 5@ a series of studies have been made to utilize the currently developed method to study fatigue failure and life prediction of unidirectional composites under off-axis loading and multilayer fiber composite laminates under in-plane cyclic loading. Also@ a major effort has been made here to address fatigue lives of fiber composite laminate tubular components subjected to combined cyclic axial loading and internal pressure. The results clearly demonstrate that the present approach are capable to evaluate the composite fatigue failure strength and life with significant accuracy and confidence.