In the traditional standard of internal friction measurement the torsion pendulum and vibration reed were preferentially recommended where the issue of strain amplitude dependence of internal friction was not concerned. To more precisely measure the internal friction and modulus at various strain amplitude, in this paper the strain amplitude dependence of internal friction and modulus is considered by analyzing the stress distribution in the sample in different internal friction measurement methods. The formulas for the measurement of internal friction and modulus versus strain-amplitude are obtained by re-deriving the principal equations for internal friction and modulus measurements by torsion pendulum and vibration reed methods from the basic definition of internal friction. This provides a new standard for precise measurement of internal friction at different strain-amplitude in the cases of high strain-amplitude excitation or high damping materials where amplitude dependent effects always appear.