For many applications, digital beamformers require an input rate which is significantly higher than that required for waveform reconstruction to achieve an adequate set of synchronous beams. Typically, this high rate is realized in the A/D conversion of the sensor outputs. A novel alternative, discussed in this paper, is to sample the sensors at a rate consistent with the Nyquist criterion and implement vernier beamformer delays by digital interpolation. This technique, which is referred to as digital interpolation beamforming, permits an efficient partitioning between A/D converter and cable bandwidth requirements and digital processing complexity. The basic structure of an interpolation beamformer is presented. It is shown that interpolation filtering and beamforming can be interchanged to minimize digital processing. Beam-pattern degradation due to interpolation error is derived and interpreted for the special case of a line array.