PurposeThis paper presents a review concerning the analytical and inverse methods of small punch creep test (SPCT) in order to evaluate the mechanical property of component material at elevated temperature.Design/methodology/approachIn this work, the effects of temperature, specimen size and shape on material properties are mainly discussed using the finite element (FE) method. The analytical approaches including membrane stretching, empirical or semi-empirical solutions that are currently used for data interpretation have been presented.FindingsThe state-of-the-art research progress on the inverse method, such as non-linear optimization program and neutral network, is critically reviewed. The capabilities of the inverse technique, the uniqueness of the solution and future development are discussed.Originality/valueThe state-of-the-art research progress on the inverse method such as non-linear optimization program and neutral network is critically reviewed. The capabilities of the inverse technique, the uniqueness of the solution and future development are discussed.