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The geometric and atmospheric processing of airborne imagery is a complex task that involves many correction steps. Geometric correction is particularly challenging because slight movements of the aircraft and small changes in topography can have a great impact on the geographic positioning of the processed imagery. This paper focused on how uncertainty in topography, represented by a digital elevation model (DEM), propagates through the geometric correction process. We used a Monte Carlo analysis, in which, first, a geostatistical uncertainty model of the DEM was developed to simulate a large number of DEM realizations. Next, geometric correction was run for each of the simulated DEMs. The analysis of the corrected images and their variability provided valuable information about the positional accuracy of the corrected image. The method was applied to a hyperspectral image of a mountainous area in Calabria, Italy, by using the Shuttle Radar Topography Mission-DEM as the topographic information source. We found out that the uncertainty varies greatly over the whole terrain and is substantial at large off-nadir viewing angles in the across-track direction. Also, positional uncertainty is larger in rugged terrains. We conclude that Monte Carlo uncertainty propagation analysis is a valuable technique in deriving quality layers that inform end users about the positional accuracy of airborne imagery, and we recommend that it is integrated in the operational processing steps of the Processing and Archiving Facilities.