The absorption of MHD waves due to the cusp (or the slow) resonance is studied numerically and the obtained results are discussed with respect to a possible application to conditions that are typical for the solar corona. The considered configuration is composed of two homogeneous regions separated by an inhomogeneous slab through which all physical parameters of the medium change continuously according to an initially prescribed distribution. The MHD waves can propagate through one of the regions only and are being partially absorbed by the non uniform slab due to resonant processes occurring in particular locations within the slab. Computational results show that the absorption arising from the cusp resonance strongly depends on the characteristics of the driving wave. It can be close to 100\% for certain angles of incidence which indicates the possibility for an efficient local coronal heating at this resonance too. The considered resonant absorption can occur for the slow as well as for the fast magneto acoustic mode.