An improved sole construction for use in shoes. The sole construction consists of a hammock-like lattice formed of medium to high modulus polymers, or a lightweight metal alloy. The lattice substantially conforms in topography to the foot, or a weight-bearing portion thereof (such as the heel or forefoot). The lattice may be disposed on, and supported by, a resilient frame, or secured directly to the shoe upper. The lattice supports the foot while suspending it slightly, even during gait, above the interior base of the shoe. The suspended portions of the foot are thusly protected from the shock of striking a surface (such as the ground, during gait), and are gently supported while bearing a load.