An integro-differential equation is considered which arises in modelling dynamic problems of viscoelastic beams. The equation is reformulated as an abstract Cauchy problem on a Hilbert space and well-posedness of the problem is proved. The construction of approximation schemes for that problem is discussed and convergence arguments are presented making use of the semigroup theory of linear operators. Numerical results are given for an example of transverse vibrations of a cantilever linear viscoelastic beam. The results of eigenvalue calculations show the efficacy of the approximation schemes.