This paper concerns the absorption of energy from two-dimensional water waves propagating over fluid of constant depth by a wave energy converter consisting of small buoyant floating rafts constrained to move in heave motion and attached to the bed with springs and dampers. Under a shallow water approximation to the fluid motion, it is shown that spatially-varying spring and damper settings allow all of the wave energy to be absorbed from all wave frequencies. The basis of the design is a formulation of a novel type of ‘Perfectly Matched Layer’ equation which can be mapped onto a shallow water model of the wave energy converter. The theoretical predictions are tested with computations based on a full description of linearised water waves and show that near-perfect absorption persists over a wide range of wave frequencies.