From Halopedia, the Halo wiki
Although the Elephant is the only indestructible human land vehicle in Halo 3, it is possible to flip an Elephant over, unlocking an interesting and somewhat funny Easter egg. The Easter egg will say, "Hold <action button> to flip... wait, what? How did you do that?", as the Elephant weighs much more than a Spartan or Elite can flip, and that the vehicle isn't intended to achieve the speed or maneuverability necessary to flip it over in the first place. 
Methods of Elephant Flipping
Gravity Lift Method
Fusion Coil Method
First, go into Forge mode and put all the Fusion Coils and Plasma Batteries on the back of the Elephant. Set the Plasma Batteries and Fusion Coils settings so every number is the highest possible. Then stand back and shoot one of the Fusion Coils and wait until the Elephant lands. An alternative method is to go into Forge mode and drive the Elephant, parking it in such a way that there is a lot of room to one side. Place about ten Fusion Coils or Plasma Batteries at the opposite side in the gap between the treads. Set the run time minimum of the explosives to the same number as placed on the map. Shoot the explosives, and the Elephant will flip to one side.
Run Over Method
Another way of flipping an Elephant is to drive one towards and partially over the other, then get out and drive the other one forward until it flips the first one over.
Take an Elephant up to the opposite side of the "alley" from the wrecked phantom, turn to face it, and drive up the right-hand structure, making sure the left-side tracks are on the ground, and the right-side tracks are on top of the aforementioned structure. Then, simply drive forward, making sure not to slip off the structure, until the Elephant overbalances and tips over. Fair warning to those on the ground: Once it tips over, gravity will speed it up to the point of potentially causing a splatter (or betrayal) should you be on foot.
Forge and Drop Pod
Go into Forge and place a drop pod. Take the drop pod and put it inside the cockpit and fly up. The Elephant will either fly up in the air, or the drop pod will slip out, and you will have to do this again. You can help reduce the risk of the latter by having the Elephant face up a hill.
Scorpion Key Method
Spawn a Scorpion and, like a key, slide it in the cargo hold of the elephant. Now turn your giant makeshift tank-shaped key upside down, and the Elephant will follow.
Just go into Sandbox or Avalanche and spawn an Elephant upside down.
Elephant Glitching in Matchmaking [No Forge/Modification]
Sometimes, in matchmaking or large custom games, the Elephant will begin to sink into the ground because of the bump, a glitch in the Halo 3 graphics engine. When objects begin to sink in the ground, they will be forced back out. The reason why they sink is most likely caused by lag.
In the case of the Elephant, when it sinks too much, it will be shot out of the ground and the Elephant will be sent flying. Usually, it will not be sent too high, but in cases of extreme lag, it can be shot all the way across the map. At times this can cause absolute havoc, causing the Elephant to crush players and vehicles, or send them flying.
The Scorpion could also spawn interlocked with the Elephant, and the overlapping hitboxes, coupled with not enough room in the cargo hold for the tank, will cause a feedback loop. The two vehicles will eventually pop free in violent fashion, potentially sending them flying. The Scorpion might actually get caught in the cargo hold and make the Elephant propel forward.
If the Elephant is flipped, then made a static object by using teleporters, vehicles such as warthogs can be put underneath, then have the elephant flipped by using RB, the vehicle will be launched out of the bottom at high speed. This is known as the "Elephant Cannon".