This paper presents the modeling and design of multiphase coupled inductors with an inductance dual model. Existing models for multiwinding coupled magnetics are reviewed and compared. These models represent identical physical relationships, but reveal different fundamentals and offer distinct design insights. The inductance dual model is particularly suited to the design of high-density, low-loss coupled inductors for multiphase buck converters. A step-by-step procedure for designing coupled inductors based on the inductance dual model is introduced. This procedure is used to design a baseline coupled inductor for a multiphase buck converter. Starting from the baseline design, an optimal procedure is conducted targeting a revised design with improved performance and reduced size. The two designs are compared by experimental measurements. The optimal design procedure reduces the inductor height from 11.5 mm to 5.25 mm, reduces the core loss from 490 mW to 240 mW, and improves the output current slew rate from 1.04 A/ns to 2.08 A/ns.