My friend Elk's sons have killed a number of elk with the 7mm-08, no losses, no problem. I do not have the same amount of experience with the 7mm-08, but have killed a lot of game with the 7x57 (same ballistics) including wildebeest, kudu and moose, also with no problem. The longest range had been around 250 yards on big stuff (have shot smaller animals to 400) but I have a hard time imagining any would have survived if shot at 300 or more. A hole through both lungs generally does it.
