Thickness of colluvium or regolith overlying bedrock or other consolidated materials is a major factor in determining stability of unconsolidated earth materials on steep slopes. Many efforts to model spatially distributed slope stability, for example to assess susceptibility to shallow landslides, have relied on estimates of constant thickness, constant depth, or simple models of thickness (or depth) based on slope and other topographic variables. Assumptions of constant depth or thickness rarely give satisfactory results. Geomorphologists have devised a number of different models to represent the spatial variability of regolith depth and applied them to various settings. I have applied some of these models that can be implemented numerically to different study areas with different types of terrain and tested the results against available depth measurements and landslide inventories. The areas include crystalline rocks of the Colorado Front Range, and gently dipping sedimentary rocks of the Oregon Coast Range. Model performance varies with model, terrain type, and with quality of the input topographic data. Steps in contour-derived 10-m digital elevation models (DEMs) introduce significant errors into the predicted distribution of regolith and landslides. Scan lines, facets, and other artifacts further degrade DEMs and model predictions. Resampling to a lower grid-cell resolution can mitigate effects of facets in lidar DEMs of areas where dense forest severely limits ground returns. Due to its higher accuracy and ability to penetrate vegetation, lidar-derived topography produces more realistic distributions of cover and potential landslides than conventional photogrammetrically derived topographic data.