Abstract <p>The initial boundary value problem regarding vibrations of an annular membrane is considered. Nonsteady boundary conditions are specified, and there is no distributed load. This is a nonclassical formulation, since rigid attachment conditions at the edges are usually specified. By appropriate replacement of the function to be determined, the initial problem may be reduced to an inhomogeneous problem with trivial boundary conditions of general form. Application of the standard Fourier method then allows us to express the solution as a functional series based on linear combinations of Bessel functions of the first and second kinds.</p>