Small specimen creep testing technique has become a hot topic of research as bulk materials are not available in many occasions. The stress distributions in the small specimens such as small punch and 3‐point bending specimens are essentially nonuniform. As it is known, the creep deformation/damage accumulation mechanisms exhibited at a high stress regime are not the same as the ones at a lower stress regime for many engineering alloys. The potential measurement errors because of stress regime‐dependent creep behaviour, however, has not been considered in the determination of the creep parameters based on small specimen testing in the previous studies. In this paper, 2 kinds of materials that show different Norton's parameters at the corresponding stress regimes are examined. A simple case of 2‐bar structure is firstly adopted to illustrate the measurement error of creep strain rate because of stress regime‐dependent creep behaviour. Furthermore, clamped beam bending testing and small punch testing are investigated to demonstrate the significance of measurement error using the same materials. It is shown that an error of more than 8 times may occur near the transition point of creep deformation mechanism depending on specimen types and materials. Attention should thus be paid to the selection of stress level in the small specimen testing to avoid significant measurement errors.