Despite encounter rates being a key component of kill rate, few studies of large carnivore predation have quantified encounter rates with prey, the factors that influence them, and the relationship between encounter rate and kill rate. The study’s primary motivation was to determine the relationship between prey density and encounter rate in understanding the mechanism behind the functional response. Elk (Cervus elaphus Linnaeus, 1758) population decline and variable weather in northern Yellowstone National Park provided an opportunity to examine how these factors influenced wolf (Canis lupus Linnaeus, 1758) encounter rates with elk. We explored how factors associated with wolf kill rate and encounter rate in other systems (season, elk density, elk group density, average elk group size, snow depth, wolf pack size, and territory size) influenced wolf–elk encounter rate in Yellowstone National Park. Elk density was the only factor significantly correlated with wolf–elk encounter rate, and we found a nonlinear density-dependent relationship that may be a mechanism for a functional response in this system. Encounter rate was correlated with number of elk killed during early winter but not late winter. Weak effects of snow depth and elk group size on encounter rate suggest that these factors influence kill rate via hunting success because kill rate is the product of hunting success and encounter rate.