For riveted joints with eccentricities of the load path, bending moments referred to as secondary bending are induced under nominally tensile loading conditions. Two simple theoretical models proposed in the literature to estimate the associated bending stresses are evaluated in the paper. Both approaches have been implemented in computer programs and applied to estimate the effect of several variables on the calculated bending stresses in the lap joint. Possibilities of the experimental and numerical verification of the models are also considered. Finally, a correlation between the secondary bending computed by one of the simple models and the observed fatigue properties of riveted specimens, as reported in the literature, is investigated. It is shown that deviations of the experimental results from the theoretical expectations stem from additional to secondary bending factors, like the inhomogeneous load transmission through the joint and the residual stresses induced by riveting process. These phenomena are known to be relevant to the fatigue behaviour of riveted joints, but they are not accounted for by the simple models. A conclusion from the present study is that despite the limitations and approximations inherent in the simple models, they provide reliable estimates of nominal bending stresses at the critical rivet rows and can be utilized in currently used semi-empirical concepts for predictions on the fatigue life of riveted joints.