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Diffusion controlled cavity growth models tend to exaggerate the growth rate. For this reason it is essential to take into account the restrictions caused by creep rate of the surrounding material, so called constrained growth. This has the consequence that the stress that the cavities are exposed to is reduced in comparison to the applied creep stress. Previous constrained growth models have been based on linear viscoplasticity. To avoid this limitation a new model for constrained growth has been formulated. Part of the work is based on a FEM study of expanding cavities in a creeping material. Compared with the previous constrained cavity growth models, the modified one gives lower reduced stresses and thereby lower cavity growth rates. By using recently developed cavity nucleation models, the modified creep cavity growth model can predict the cavity growth behaviour quantitatively for different types of austenitic stainless steels, such as 18Cr10Ni, 17Cr12NiNb and 17Cr12NiTi. [ABSTRACT FROM AUTHOR]