While the applications of Geographic Information Systems (GIS) have progressed from a descriptive tool to a decision making and modeling tool, the understanding of errors and variability of the components of a GIS has lagged behind. Slope is one of these components. This dissertation evaluates different methods for determining and characterizing slope values in polygons and how these methods affect natural resource models. Eight different previously used methods for determining cell slope values were compared using elevation data from the USGS Big Stone Gap, Virginia, Digital Elevation Model. The 28 pairwise comparisons were statistically different, but for practical applications six of the comparisons were similar with an average slope difference of less than one percent. In a decision model the effect of changing just the slope method used to determine cell slope values can influence the results of a model enough to cause almost a 10 fold difference. Since usually the smallest administered unit in natural resource management is the stand (polygon), nine ways of describing the slope of a polygon for 240 polygons using an aggregation of cell slope values were investigated. These polygon descriptors were mean, trim mean, median, mode, first quartile, third quartile, standard deviation, minimum and maximum cell slope value. Also, a new method of determining polygon slope was examined using trend surface techniques, which is not based on aggregation of single cell slope values. The distributions of cell slope values in a polygon cannot be assumed normal since few polygons had a normal distribution. The sensitivity of these polygon slope descriptors to polygon area and surface complexity, based on fractal dimension, was examined and found not to affect these polygon characteristics. The application and logical decisions required to choose an appropriate slope method and polygon slope descriptor(s) based on model objectives are shown in two examples, a harvesting and USLE model. Automating the process of choosing the appropriate polygon slope descriptor(s) and how to integrate these methods in an operational GIS using an Expert System is discussed. / Ph. D.