Concepts envisioned for the future of civil air transport consist of unconventional propulsion systems in the close proximity of the airframe. Distributed propulsion system with exhaust configurations that resemble a high aspect ratio rectangular jet are among geometries of interest. Nearby solid surfaces could provide noise shielding for the purpose of reduced community noise. Interaction of high-speed jet exhaust with structure could also generate new sources of sound as a result of flow scrubbing past the structure, and or scattered noise from sharp edges. The present study provides a theoretical framework to predict the scrubbing noise component from a high aspect ratio rectangular exhaust in proximity of a solid surface. The analysis uses the Greens function (GF) to the variable density Pridmore-Brown equation in a transversely sheared mean flow. Sources of sound are defined as the auto-covariance function of second-rank velocity fluctuations in the jet plume, and are modeled using a RANS-based acoustic analogy approach. Acoustic predictions are presented in an 8:1 aspect ratio rectangular exhaust at three subsonic Mach numbers. The effect of nearby surface on the scrubbing noise component is shown on both reflected and shielded sides of the plate.