The Small Punch Creep Tests (SP-C tests) are simulated by a Finite Element Method (FEM). The objective of the present study is to establish a foundation for the SP-C test method by investigating the deformation and stress state of the SP-C test specimen. The emphasis is placed on the dependence relation of the creep strain and the stress on the measurable quantities, such as applied loads and the central deflections. Simulation works are conducted for two different materials, one is the tungsten-alloyed 9% Cr ferritic steel and the other is 12Cr1MoV steel. The numerical results for the central deflection versus time curves are quantitatively similar to the experimental results obtained on tungsten-alloyed 9% Cr ferritic steels. From the numerical results, the relationship between the central deflection and the equivalent creep strain is approximately independent of load, temperature, and material properties. The magnitude of the equivalent stress in the central region of the SP-C specimen shows no significant change with respect to time at the secondary creep stage, an approximate equation is proposed for the assessment of the equivalent stress in the SP-C specimen. As a farther result, the high temperature creep properties of the 12Cr1MoV steel and tungsten-alloyed 9% Cr ferritic steel are appraised by numerical simulation. The results are in good agreement with the results from the standard test method. The results indicate that the small punch test technique is an effective method for the evaluation of the high-temperature creep properties of materials.