A variational-difference method is applied to solve dynamic contact problems with contact domains of arbitrary planform, where the tedium in realizing this method is reduced substantially while the convergence is improved by the selection of delt-like functions of a special kind as coordinate functions. Results of numerical investigations are presented for the vibrations of a system of massive rectangular stamps on an elastic bed. The presence of resonance frequencies whose values depend on the size and mass of the stamps, and the presence of a shielding effect when a surface wave runs over the system of stamps are clarified. The vibrations of a massive foundation of rectangular planform were investigaged earlier /1/, as were the vibrations of a system of two massive rectangular foundations /2/. However, the approaches used possess worse convergence, compared with the variational-difference method, and require the evaluation of double integrals of strongly oscillating functions. As noted in /3/ in particular, this disadvantage is inherent in all methods based on the partition of the contact domain into cells with a uniform stress distribution therein.