A mathematical model of the propagation of acoustic shear waves in muscle tissue is considered. The muscle is modelled by an incompressible transversely isotropic viscoelastic continuum with quasi-one-dimensional active tension. Two types of shear waves in an infinite medium have been established. The waves of the second type (transverse) propagate without attenuation even when myofibril viscosity is taken into account. A problem of standing transverse waves in a rectangular layer has been investigated numerically. The values of the problem parameters have been found for which the active tension or muscle tonus is easily estimated from the characteristics of standing waves. This value is informative for the diagnosis of muscle state.