We have found a mistake in the classical oscillation equation for a round membrane [1] attributed to the kind of interactions. Correction of an erroneous idea regarding the nature of the impact and substitution of tensile forces by tensile stresses provides us to derive the equations of small transverse oscillations of circular membrane with allowance for mechanical and rheological characteristics of the membrane. We derived the oscillation equation for a homogeneous circular membrane and determined its Eigen frequency taking into account the mechanical and rheological properties of the membrane material. Solution of a differential equation by the Fourier method requires an additional change of variables to avoid incorrect results when calculating Eigen frequencies. The oscillation equation for a circular membrane and Eigen frequencies are obtained as function of the component concentration in the case of linear elastic composite material. Recommendations regarding taking into account the creep value of the composite material of the membrane are specified proceeding from the technical theory of aging. It was found that the calculation of the effective characteristics of the membrane material in accordance with the Voigt hypothesis corresponds to the solution of the problem of averaging set for horizontally layered membrane. Application of Reiss hypothesis corresponds to oscillations of vertical coaxial layered or vertically fibrous membrane, whereas application of Kravchuk-Tarasyuk method to narrowing of the Reuss-Voigt “range” corresponds to the best approximation of the effective properties of structurally inhomogeneous composite membrane.