The computational domain is artificially designed in the numerical simulation of elastic waves propagating in unbounded media. As a result, boundary reflections arise from the edges of such truncated models. Although many complex schemes have been developed to solve this problem, the absorbing boundary technique of Cerjan et al (1985 Geophysics 50 705–8), as the simplest, is still widely used, especially for the pseudospectral method. To improve the efficiency of suppressing such boundary reflections in the simple technique, we apply damping to the movement velocity of nodes in a narrow strip along the edges. Several modelling results demonstrate its greater effectiveness than previous treatments which apply the damping to the displacement or both displacement and movement velocity of nodes.