1. Lung Shot: Follow the rear portion of the front leg about 30% up the animal's body to hit the middle of the lungs. This large area will likely yield a moderate to high lung shot, which enables the lower lungs to fillup with blood and the drowning of the animal in short order (not immediately).
2. Heart & Lung Shot: Some precision shooters prefer to hold as close to the shoulder as possible (1:00 position) for both a heart and double lung shot - aiming 1" above and 1" behind the front leg - taking out the top of the heart and the lower lungs. Note: Big Game animals have hearts that sit low in the body cavity and are 1/2 way shielded by the shoulder joint.
Circulatory System - Heart & Lungs
3. Base of Neck / Spine Area: Follow the forward portion of the front leg about 2/3'rds up the animal's body to where the neck meets the spine. There are a lot of major support bones in this area that when broken, will anchor the animal very quickly. While this is a decent sized kill zone for the more experienced hunter, it's not as large as the lung area.
Bow & Arrow
For a lung shot, follow the rear portion of the front leg about 40% up the animal's body. Aiming near the broad center of the body allows for a greater margin of error, which might be needed depending on your skill. This large area will likely yield a high lung shot, which enables the lower lungs to fillup with blood and the drowning of the animal in short order (not immediately).
See also: Elk Anatomy Overview.