A field of application for the convolution quadrature method are time dependent integral equations. Here, the integral equation for a transient excited viscoelastically supported Euler-Bernoulli beam will be deduced and solved with the convolution quadrature method. A direct evaluation in time domain is only possible without the viscoelastic foundation, however, the resulting time stepping procedure is not stable [67]. Also, the time-dependent fundamental solutions for the beam theory needed to solve directly in time domain contain Fresnel integrals. Both points, unstable time stepping procedure and complicated time-dependent fundamental solutions, give reason to use the convolution quadrature method. Moreover, except by means of the convolution quadrature method, for the beam on a viscoelastic foundation there is no possibility to establish a formulation in time domain since no time-dependent fundamental solution is known.