Can't speak for African buffalo, but the best shot placement on Asiatic buff (which are often larger in the body) is the point of the shoulder. Over .40-cal cartridges are recommended, and premium bullets are mandatory.

I use .400 x 3-inch NE with 400gr Woodleigh softs, .416 Taylor with 410gr Woodleigh softs, .577 Light Nitro with 650gr Woodleigh softs, or .470 with 500gr Woodleigh softs.

The shoulder-shot with a bonded-core soft-point will break one or both shoulders, maybe break the spine where it dips down between the shoulder-blades or at the base of the neck, wreck the top of the heart or the big arteries at least, and almost certainly catch both lungs. More margin for error than any other side-on shot too, IMHO.

Works for me!

No experience with ele, but assume solids would be mandatory, which could make a difference.