The Last Hero said:
That's the advantage of space. It's big enough to hold, practically anything, and so, eventually, it does. People think that it is strange to have a turtle ten thousand miles long and an elephant more than, two thousand miles tall, which just shows that the human brain is ill-adapted for thinking and was probably originally designed for cooling the blood.
The Folklore of Discworld said:
(In comparison, the Disc is only 10,000 miles wide.)
The Science of Discworld said:
Unfortunately for this theory, it was known on other grounds that Discworld is some 10,000 miles (16,000 km) from rim to rim.
The Great A'tuin lifts the Disc and the four elephants every second of every minute of every day of every year of every decade of every century of every millenia of every aeon of it's lifespan. The Disc is 16,000km (16000000m) in diameter, or a radius of 8000km (8000000m). The Disc is about 30 miles (48.28032km, or 48280.32m) thick at the rim and thicker in the middle by an unknown amount (the average thickness of continental plates is about 200km, or 200000m, so let's go with that). We'll get the volume as a cone and a cylinder, then add them together.

h = 200000m - 48280.32m
= 151719.68m

V = πr^2h/3
= π X 8000000^2 X 151719.68/3
= 1.01683506e19m^3

V = πr^2h
= π X 8000000^2 X 48280.32m
= 9.70733431e18m^3

V = 1.01683506e19 + 9.70733431e18
= 1.98756849e19m^3

Density of the Earth per m^3 is 5,515.3kg.

M = 1.98756849e19 X 5515.3
= 1.09620365e23kg

Let's get the GBE for this.

Centre of gravity = 200000m/3 = 66666.6667m X 2 = 133333.333m
Earths Gravity Pull = 9.807m/s²
Mass = 1.09620365e23kg

E = 133333.333m X 9.807 X 1.09620365e23kg
= 1.43339589e29 joules
= 34.2589839866 exatons

Impressive, but we're not done yet! There's also the four Elephants. The average height of an Asian elephant is 2.7m, while the average height of an African elephant is 3.3m, which averages out at 3m. The Asian elephant on average weighs 5400kg while the African bush elephant on average weights 6000kg, which averages out at 5700kg. In the foremost quote, the elephants are each 2000 miles (3218.688km, or 3218688m) tall.

M2 = (H2/H1)^3*M1
= (3218688/3)^3*5700
= 7.03959597e21kg

There's four of them, so times it by 4.

Not sure where the centre of gravity on an elephant is exactly, but it'd be somewhere in the main body, so let's go with two thirds of the way up.

Centre of gravity = 3218688m/3 = 1072896m X 2 = 2145792m
Earths Gravity Pull = 9.807m/s²
Mass = 2.81583839e22kg

E = 2145792 X 9.807 X 7.03959597e21
= 1.48139724e29 joules
= 35.4062437859 exatons

There's four of them, so times it by 4.

E = 1.48139724e29 X 4
= 5.92558896e29 joules
= 141.624975143 exatons

E = 34.2589839866 exatons + 141.624975143 exatons
= 175.883959 exotons

Final Results

The Great A'tuin lifts the Disc = 175.884 exotons

The Great A'tuin does this every day endlessly and effortlessly. And this is still far off the true energy for two reasons. The first is that we still have to add the speed, and the second is that the elephants are seemingly made of metals.
The 5th Elephant said:
They say the world is flat and supported on the back of four elephants who themselves stand on the back of a giant turtle
They say that the elephants, being such huge beasts, have bones of rock and iron, and nerves of gold for better conductivity over long distances.*
They say that the fifth elephant came screaming and trumpeting through the atmosphere of the young world all those years ago and landed hard enough to split continents and raise mountains.
No one actually saw it land, which raised the interesting philosophical question: when millions of tons of angry elephant come spinning through the sky, and there is no one to hear it, does it - philosophically speaking - make a noise?
And if there was no one to see it hit, did it actually hit?
*not rock and iron in their dead form, as they are now, but living rock and iron. The dwarfs have quite an inventive mythology about minerals.