The Small Punch (SP) test with constant deflection rate is a miniature technique that can provide estimates on the material tensile properties. Linear correlations are usually used for relating the maximum force and displacement at maximum force, recorded during the SP test, to the ultimate tensile strength. Fitting coefficients used in the correlations are calibrated on data from flat SP specimens. SP test requires only a small amount of testing material which represents a clear benefit when irradiated samples have to be tested. Therefore, there is a considerable interest in using SP for testing fuel cladding material properties. In this study we show that the same correlation equations, albeit with adjusted fitting coefficients, can be used to estimate the ultimate tensile strength from tube SP specimens made out of P91 ferritic/martensitic and 15-15Ti austenitic stainless steel. The calculated fitting coefficients lead to reasonable estimates of the ultimate tensile strength at temperatures of up to 650 C although the coefficients themselves have been computed at room temperature. The coefficients are more suited for assessing ductile materials as the models used for computing the coefficients do not take into account damage (degradation of the material stiffness) or crack initiation and propagation, observed during the SP tests of brittle material. Finally, using the calculated ratios of maximum forces and displacements at maximum forces, one can map the two values of a given curved SP test to the equivalent flat SP values.