The Gurson-Tvergaard-Needleman damage model is implemented in Small Punch (SP) finite element model with the purpose of evaluating the influence of crack initialization and propagation on the SP force–displacement (F v) curves and the maximum force, Fm, which is used for estimating the Rm. Five materials, significantly different in Rm and ductility are investigated. Numerical calculations are performed and compared to the experimental measurements to evaluate the accuracy of the model. It is shown that the model is capable of capturing crack initialization in cold worked 15-15Ti stainless steel samples with different levels of ductility, both in terms of the number of cracks and their positions. For these two materials and the more ductile P91, P92 ferritic/ martensitic steels, the simulations indicate significant impact of damage on the F v curves in the vicinity of the maximal force, Fm. This can significantly influence the estimation of Rm from the Fm and vm points. However, the model tends to predict the crack initialization at a larger displacement compared to the experiments.