A detailed evaluation on the method of internal friction measurement by the stress-strain hysteresis loop method from 0.01 to 1 Hz at 10-8 to 10-7 strain amplitude and 23.9 ¿C is presented. Significant systematic errors in relative phase measurement can result from convex end surfaces of the sample and stress sensor and from end surface irregularities such as nicks and asperities. Preparation of concave end surfaces polished to optical smoothness having a radius of curvature >3.6¿104 cm reduces the systematic error in relative phase measurements to <(5.5¿2.2)¿10-4 radians. The values of Q-1E (internal friction under uniaxial compression) determined from the relative phase measurements are ‖ Q-1E -Q-1S‖ <2.8¿10-3 for the tool steel sample and ‖ Q-1E -Q-1S‖ <2.2¿10-3 for the Westerly granite sample, where Q-1S is the internal friction of the fused quartz stress sensor under uniaxial compression. These values are consistent with those inferred from the relative modulus dispersion data also presented in this paper. The polymethyl methacrylate (PMM, trade name Plexiglass) sample shows high values of internal friction (Q-1E ≂5¿10-2) with strong frequency dependence and with a maximum in Q-1E at ≂0.4 Hz.