Wolf-prey research has focused on single-prey systems in North America dominated by moose (Alces alces) or white-tailed deer (Odocoileus virginianus). Elk (Cervus elaphus) are social ungulates and the main prey item of wolves (Canis lupus) in Banff National Park (BNP), Alberta. Grouping behaviour may affect the functional response of predators by changing how predators encounter and kill prey. We studied wolf predation on elk in BNP during the winters of 1997-1998 and 1998-1999 and tested how elk group size affected the availability of and encounter rates with elk groups and attack success of wolves. Wolves encountered larger elk groups than expected based on availability, and killed more elk from large groups than expected based on numbers of encounters. Elk group size increased with elk density in BNP. Increased rates of encounter with and success of attacking large elk groups, and the positive group size - density relationship may be a mechanism for density-dependent predation. We developed a predation-risk model to test the prediction that grouping will benefit individual elk, given this predation regime. Elk appeared to adopt two different strategies to minimize predation risk: living in small herds that were rarely encountered by wolves or living in large herds that reduced their predation risk through dilution.