It's not the elephant. Two much stranger animals may stay pregnant for around three years or more, and we couldn't find a source that settles which one wins.
We found no report of anyone timing this shark's pregnancy from start to finish, so the figure is an estimate: about 3½ years, cited alongside a Japanese study that measured how fast its unborn babies grow.
A salamander of the Alps whose babies develop all the way inside their mother. Below 1,000 m3,300 ft that takes about 2 years. Up in the highest places, probably 4.
The shark's 3½ years is nearly 5 human pregnancies in a row!
In a 1990 study of 264 frilled sharks from Suruga Bay, Japan, scientists kept unborn babies in artificial conditions for up to 134 days. They grew just 10–17 mm0.39–0.67 in a month, roughly a fingernail's width. Scientists cite 3½ years alongside that growth rate. We couldn't read the full study to see how it gets from one to the other, so treat the number as an estimate, not a stopwatch reading.
The rule is simple: the higher the mother lives, the longer she waits. One forestry guide says 2 years below 1,000 m3,300 ft, 3 years between 1,000 m3,300 ft and about 2,000 m6,600 ft, and in the highest places probably 4. Another source gives 2 years at 650–1,000 m2,100–3,300 ft and 3 years at 1,400–1,700 m4,600–5,600 ft.
Both champions have a catch. For the shark, older estimates say as little as 1 to 2 years. For the salamander, the 4 is a "probably". Until the figures firm up, it's a photo finish.
Frilled shark photo: saname777 from Tokyo, Japan, CC BY 2.0, via Wikimedia Commons · Alpine salamander photo: böhringer friedrich, CC BY-SA 2.5, via Wikimedia Commons