Cows do not sleep standing up. In order to rest, cows lie down in one of two ways: either resting on their sides or with their chests upright in a catlike fashion.
The idea that cows sleep while standing is primarily used to support the urban myth known as cow tipping. While many people claim to have tipped over sleeping cows as the animals slept standing, according to the Manitoba Veterinary Medical Association, such boasts have been proven false since cows do not sleep while standing as horses do. Pushing a standing cow over would also be very difficult for the average person to accomplish due to the cow's weight.