Current standards (as an example, DNV-OS-E301[1] and API-RP-2SK[2]) do not account for mean load in the fatigue assessment of mooring chains. Both standards, provide S-N curves derived from experimental work without specifying the mean load for which they have been obtained or proposing a mean load correction function. This paper reports a fatigue analysis study of mooring chains under Tension Loading using a multiaxial fatigue criterion for two different mean loads. Multiaxial fatigue criteria enable to account directly for complex phenomena, such as residual stresses, non-proportionality of the stress tensor, among others. This paper presents an example of the implementation of the Dang Van fatigue criterion for studying the fatigue behavior of mooring chains under tension. It quantifies the effect of the mean load on the fatigue lifetime and the failure location. Furthermore, it also proposes a simplified approach to reduce the complexity and the computational time of the fatigue analysis using Dang Van fatigue criterion. The paper is organized as follows: in the first part an example of the fatigue assessment is reported. Two different loading conditions with the same load amplitude but different mean loads are studied. The assessment method is based on two steps: a mechanical analysis and a fatigue analysis. In the second part, a simplified fatigue assessment method is proposed. As part of this method, a ratio between the fatigue lifetimes of two loading conditions, which have the same load amplitude but different mean load, is formulated. This ratio has been obtained analytically using the geometric representation of the Dang Van fatigue Criterion. Finally, the paper ends with a discussion, based on recent works, regarding the formulation of the locus of the Dang Van criterion and the fatigue properties used for the calibration of this criterion.