A theoretical analysis is given of mechanical wave processes in muscle tissue over a broad frequency range. As in /1/, the elastic waves are studied using a continual chemomechanical model /2–5/ extended to the case of an arbitrary discrete and continuous relaxation time spectrum /6/. Analytic expressions containing elastic and viscous parameters, as well as parameters corresponding to the muscle anisotropy and activity, are obtained for the elastic wave velocity and damping in thin muscle tissue specimens. The muscle specimen stability conditions are found. A comparison is made with known experimental results and it is shown that the model constructed describes the elastic-wave characteristics satisfactorily in a muscle in different states. Investigation of elastic-waves in a medium is an important (often unique) method of determining its structure and rheological and functional properties. This especially concerns media of a biological nature, particularly muscle and internal organ tissues. As a rule, biological media are anisotropic and heterogeneous, where the muscle tissue still manifest active properties, and develops a stress as a result of chemical reactions. During miscle contraction (single, say) the elastic-wave velocity and damping depend on the muscle stress and degree of contraction. Depending on the wavelength, the excitation method, and the propagation direction, mechanical waves of different types are possible in which the structural and rheological properties of the medium appear differently. If the wavelength is small compared with the characteristic linear dimensions of the tissue specimen, longitudinal waves are possible that are due to the compressibility and propagate at different angles to the anisotropy axes, as are also transverse (shear) waves. As they apply to muscle tissue, these kinds of waves were examined in /1, 2, 7/. The longitudinal wave damping, unlike their velocity, depends strongly on the state of the muscle and the propgation direction (along or across the fibres) /1, 8/. Longitudinal /6/ and flexural displacement waves, as well as torsional waves are possible in specimens that are thin compared with the wavelength. Longitudinal and flexural waves are also possible in specimens in the form of thin plates whose thickness is small compared with the wavelength while the dimensions in the two other directions are large. Surface (Rayleigh) waves and some others are also of interest.