Generally speaking, the elk is an herbivore. In other words, it eats plants. More specifically, it looks for grasses and forbs in the summer, grasses in the spring and fall, and grasses, shrubs, tree bark, twigs and whatever else it can find to eat in the winter. Additionally, it may supplement its diet at licks where it can take in minerals that help grow healthy coats and produce nutritious milk.
Having said that, some elk and deer are known to occasionally venture outside their usual menus in search of eggs or, yes, meat.
This video recently posted by Good Bull Outdoors shows a cow elk chase a couple of Canadian geese and a group of goslings before eventually scooping up one of the little ones and chewing on it.
(Video source: Good Bull Outdoors)