Various techniques are proposed for reproducing the elastic wave propagation in an unbounded medium such as the infinite elements, the absorbing boundary conditions, or the perfect matched layers. Here, a simplified approach is adopted by considering absorbing layers characterized by the viscous Rayleigh matrix previously studied by some authors. Further improvements to this procedure are provided. First, we start by establishing the strong form for the elastic wave propagation in a medium characterized by the Rayleigh matrix. This strong form will be used for deriving optimal conditions for damping out in the most efficient way the incident waves while seeking to avoid the spurious reflected waves at the interface between the domain of interest and the Rayleigh damping layer. A procedure for designing the absorbing layer is proposed by targeting a performance criterion expressed in terms of logarithmic decrement of wave amplitude in the layer thickness. A multi‐layer strategy is proposed to improve the efficiency of the absorbing boundary layer. The coupling GC method is used to carry out explicit/implicit co‐computations, making interact in time an explicit time integration scheme for the domain of interest with an implicit time integration scheme for the absorbing boundary layer. Efficiency of this approach in term of accuracy and CPU time is shown in 1D and 2D elastic wave propagation problems. Copyright © 2015 John Wiley & Sons, Ltd.