A detailed evaluation on the method of internal friction measurement by the stress-strain hysteresis loop method from 0.01 to 1 Hz at 10-8-10-7 strain amplitude and 23.9oC 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 >3.6X104 cm reduces the systematic error in relative phase measurements to <(5.5+ or -2.2)X10-4 radians. -from Authors