The problem of measuring relative relaxation strength of the order of 10-4-10-2 has been solved by using an electrodynamic balance with a resolution of 10-6. It has been modified in order to load the free side of a bending sample clamped on the other side by lifting or sinking the scale of the balance. The weight is fully supported by the scale and the sample. After loading the sample, its relaxing stress can be calculated using the time-dependent reading of the balance. This measuring technique is well suited to the problem of finding materials with low relaxation strength for balance applications, because the measuring conditions such as stress level, stress resolution, range of measuring time and mode of relaxation are nearly the same as the relaxation conditions in the balance.