We study the influence of surface roughness on the infrared reststrahlen band in insulating materials. We model the surface features with either truncated spherical bumps on, or truncated spherical pits in, the substrate. The polarizability of the truncated sphere-substrate system has been calculated from a multipolar expansion, taking into account up to 16 orders. Two types of resonance have been identified. Substrate-related absorption peaks occur at the transverse optical or longitudinal optical phonon frequency, depending on the direction of the incident electric field. Additional absorption peaks occur in the vicinity of the resonance frequency of a sphere. They are dependent on the detailed geometrical configuration.