Unlike the uniaxial creep test results, the interpretation of small punch (SP) test results is not straightforward due to the complex deformation behavior of SP specimens. Accordingly, the reliability of correlations of SP creep test results with corresponding uniaxial tests is still not clear. One crucial point is that the initial yielding at the beginning of an SP creep test results in the hardening of the material before creep sets in and is thought to affect the creep properties. In this study, to clarify this effect, first an accurate numerical model of the SP creep test has been developed following which this model was used to study the influence of test parameters such as specimen thickness, punch diameter and the radius of the receiving hole on the initial yielding. Varying these parameters changes the deformation mechanisms and thus has a strong effect on the deflection-time curves along with the amount of initial plastic deformation. It was observed that decreasing specimen thickness and the punch diameter increased the initial yielding. Conversely, increasing the radius of the receiving hole resulted in higher initial yielding.