This paper develops the foundational framework for three-dimensional (3D) near-field beamfocusing, termed as volumetric near-field beamfocusing, using uniform rectangular arrays (URAs). We first analyze matched filter (MF) beam-forming, and derive closed-form expressions for the lateral and axial resolutions around a target focal point. The analysis reveals that MF achieves strong lateral intensity but inherently produces an axially elongated focal region, which limits its compact volumetric energy concentration. This demonstrates that existing beamfocusing techniques in literature are primarily two-dimensional (2D) beamfocusing or spot beams, not truly 3D focused beams. To overcome this, we introduce a novel Zernike-based phase tapering approach, inspired by optical aberration correction. By incorporating fourth-order Zernike modes, the extended axial structure is reshaped into a sharper volumetric focus. Both analytical derivations and numerical simulations with URAs of practical dimensions confirm that Zernike-based tapering enhances volumetric focusing and reduces focal depth (approximately up to 73 times) and incurs only a moderate reduction in peak intensity (approximately 1.5 dB) compared to conventional MF. These findings establish phase-domain tapering via Zernike polynomials as a foundational tool for compact volumetric beamfocusing. It also opens up a plethora of promising applications for near-field wireless communications, sensing, and localization systems that require precise energy confinement in three dimensions.