This paper presents results of a numerical study on the effectiveness of open trenches in reducing the ground vibration caused by propagating Rayleigh waves. The analysis is performed in the frequency domain and under conditions of plane strain using the Boundary Element Method. The soil is modelled as a homogeneous isotropic linear elastic half space. In order to represent the screening effect due to the installation of the barrier, the index ER is introduced. ER is defined as the ratio of the rate of energy transmission over the area to be protected in the presence of the trench and that without the trench. By means of ER, the influence of several parameters on the screening efficiency of the trench is investigated in some detail