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To assess creep-fatigue life consumption in a high temperature component, strain ranges and stress relaxation histories are needed to be estimated. Inelastic finite element analysis may provide these structural responses. Performing inelastic FEA is, however, usually costly, and thus simple elastic FEA-route methods to estimate these are preferred to in some practical cases. A simple method employed in a design code for the Japanese proto-type fast breeder reactor uses an elastic follow-up factor, and is applicable for components subjected to cyclic secondary stresses. A cantilever model was employed to illustrate theoretical background for this method, and lead to a default value of three for gross elastic follow-up factor for the simplicity and conservatism. Validity of this method, however, has never been confirmed theoretically for general conditions of geometry, loading, and material properties. This paper describes characteristics of the factor based on theoretical investigations of a generally-shaped component subjected to a displacement-controlled loading. Some supporting numerical examples are shown by performing elastic-plastic FEA of a notched cylinder.