At the international conference on problems of internal friction (ECIFUAS-6) the problem of attaining a highly damping state of metallic ferromagnetic materials and of ensuring stability of their operational properties was extensively discussed. The conference participants presented the results of investigations of the influence of the degree of preliminary strain, of static stresses [1], of internal stresses of different origin [2] on the attainment of a highly damping state of high chromium steels.Chromium ferritic steels (known abroad as "Silentalloy") are highly damping structural materials that are very promising for widespread industrial application.In ferritic steels the main cause of attenuation of mechanical vibrations is magnetoelastic hysteresis. In ferromagnetic materials there arises, together with elastic strain Eel, an additional mechanostriction strain es under the effect of external applied stresses, which is brought about by a change of orientation of the vector of local magnetization. Overall strain is e = Eel + E s. Under the effect of reversed cyclic stresses the domain boundaries are shifted with a frequency equal to the frequency of the external vibrations, and that leads to additional energy dissipation. The losses on magnetoelastic hysteresis AW are correlated with the amplitude of the acting cyclic stresses cr by the expression AW = Do n, where D is a coefficient depending on the type of material; n < 3 [3].We investigated ferritic high chromium steels containing 0.03 % C, 25 % Cr, and 4 % Mo. The amplitudinal dependence (AD) of internal friction (IF) and the shear modulus (SM), measured according to the square of the frequency f2, in specimens with 0.8-mm diameter made of high chromium ferritic steels were determined in a wide range of temperatures (-190-820°C) and strain amplitudes ((1-140)10-5). The characteristics were measured on a reversing torsion pendulum (f -= 0.4 --1 Hz) both visually according to the number of oscillations in the selected range of strain amplitudes A2-A 1, and automatically according to the time of passage of a light beam across a constant base. The semiautomatic installation type reversing torsion pendulum has a low level of intrinsic mechanical losses in measurements [4], and its use therefore makes it possible to estimate very accurately the internal energy dissipation by the material of the specimen.For the most reliable determination of magnetoelastic absorption we used the method of measuring the characteristics of IF and of the shear modulus SM as functions of the strain amplitude 3' with their minimally possible averaging. The method of measuring IF (Q-1), f2, and 3' is based on measurement of the time intervals of the passage of a light beam, connected with