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We present a near-field plate that can generate an evanescent Bessel beam. The metallic plate consists of nonperiodic concentric corrugations that surround a coaxially fed aperture. The design procedure for such a device is outlined. The designed plate is simulated using a full-wave electromagnetic solver and is shown to produce an evanescent Bessel beam, thereby verifying its design and operation. The performance of the near-field plate is contrasted against a coaxial probe and a near-field plate designed to produce an Airy focal pattern with the same beamwidth. Such a device, capable of producing evanescent Bessel beams, will find applications in near-field probing/imaging systems, data storage, and biomedical devices.