Numerical simulation of wave propagation phenomena is a relevant subject in many different fields of science and engineering, such as, among others, geophysics, ocean acoustics, materials science and biomedical engineering. An effective modelling of wave propagation phenomena in real media requires to take into account several non-trivial but fundamental physical aspects, such as energy dissipation due to viscous effects and heterogeneous spatial distribution of material properties, which pose additional challenges from both a mathematical modelling and numerical point of view. In this work we consider a linear viscoelastic material behaviour described by means of the Kelvin-Voigt rheology. Material heterogeneity has been taken into account by dividing the domain into multiple layers, each of them being associated with a distinct material and therefore characterised by a particular set of coefficients that define its physical properties. The system of Partial Differential Equations obtained combining the Cauchy momentum equations with the Kelvin-Voigt constitutive model has been reduced from second order to first order in time by doubling the solution variables, that are the displacement and velocity fields. The weak formulation has been discretised in space by means of the Spectral/Spectral Element Method. In the latter approach the elements are the material subdomains. Then, the unknown displacement and velocity fields have been approximated by means of basis functions defined so that, when restricted to each element, they are linear combinations of either Legendre or Chebyshev polynomials. The discretisation in space of the weak formulation yields a system of Ordinary Differential Equations that are solved either by means of standard numerical time-stepping schemes or by exact integration via eigenvalue decomposition. Finally, the proposed numerical strategy has been validated by performing numerical simulations of wave propagation phenomena in homogeneous and heterogeneous materials due to the action of a point source.