A method for predicting time-dependent stresses and strains in the case of localized creep has been developed. This method is based on strain energy density considerations and is an extension of the method previously developed by the authors for localized time-independent plasticity problems. The solution method has been derived in a general form so that it may be applied to multiaxial notch tip stress states. This technique has been used to predict creep effects and the associated stress redistribution at the root of a notched zirconium alloy pipe and in a thin notched plate made of aluminum, both subjected to thermal creep. The predictions have been compared with the finite element data and good agreement obtained. The computational time for calculating the notch tip stresses and strains was much shorter than that required for the finite element analysis. The method can be particularly useful for the analysis of creep effects in the case of cyclic loading with hold times where the FEM calculations are very time consuming.