Surface subsidence resulting from the collapse of underground cavities, whether natural or man-made can interact with existing buildings on the surface. One of the mitigation measures used is to dig a peripheral trench at a certain distance from the structure, filled with a soft material, like peat, or artificial material. This is thought to reduce the horizontal strain applied to the structure. The 3D numerical analysis presented in this paper is a first step towards evaluating the efficiency of this type of mitigation technique. The numerical model developed using Abaqus allows the effect of various parameters such as the width or depth of the peripheral trench, its distance from the building and/or the stiffness and strength of the filling material to be clearly determined.