Two stress regime‐dependent creep constitutive equations, that is, two‐regime Norton (2RN) model and Sin‐hyperbolic (Sinh) model, are adopted to numerically investigate the influence of constitutive equation and friction on the measurement of steady‐state creep strain rate based on five types small specimens. Results show that the influence of constitutive equation and friction depends strongly on the type of small specimen. A measurement error of more than 19 times may occur if the 2RN model is used, while the use of the Sinh model is able to generate a consistently lower measurement error. Of all small specimens, the cantilever beam testing (CaBT) is revealed to exhibit the best comprehensive performance in terms of measurement error and response to friction. To validate numerical findings, creep tests on the CaBT specimen of P91 steel are conducted at 600°C. Finally, recommendations on the choice of small specimen for obtaining creep strain rate are made.