An analytical model of laser absorption for planar radiation on steep, high density plasma surfaces is presented. Within the constraints of classical electrodynamics, the model is valid for arbitrary intensity and incidence angle, and is insensitive to the details of the absorption mechanism. At intensities beyond 1020 W cm−2, consistently high (>50%) absorption with a flat angular dependence is found. The model's convenient closed form makes it widely applicable to laser-driven ion acceleration schemes, hard x-ray sources and the fast igniter fusion concept.