A nonlinear model is proposed for studying the effect of the eccentricity of applied tensile forces on the clamp load loss in bolted joints that were initially tightened beyond the bolt elastic limit while the joint remained in the elastic range. A closed form solution is obtained for the amount of clamp load loss due to a cyclic separating force. The proposed model takes into account two sources of nonlinearity, namely, the strain hardening behavior of the yielded bolt material as well as the nonlinear deformation behavior of the clamped plates under an external separating load. After the initial tightening of the fastener past its elastic limit, the subsequent application of a tensile separating force on the joint tends to increase the fastener tension in a nonlinear fashion, and, simultaneously, reduce the clamping force in the bolted joint from its initial value. Upon the removal of the cyclic tensile load, the bolted joint system reaches a new equilibrium point between the residual fastener tension and the joint clamping force. At the new equilibrium point, the fastener tension is reduced from its preload due to its plastic elongation; simultaneously, a partial yet permanent loss in the clamp load level takes place. Excessive clamp load loss may lead to joint leakage, fastener loosening, or fatigue failure. For a known amplitude of the external cyclic tensile load, the increase in bolt tension and corresponding reduction in the joint clamp load are highly sensitive to the eccentricity of the tensile load (from the bolt center). Variables studied include the eccentricity value of the separating load, rate of strain hardening of the bolt material, compressive and tensile stiffness of the clamped plates, bolt stiffness, bolt preload, and magnitude of the separating tensile load.