Ask about elephant ornaments and you will be told, with some confidence, that the trunk must point upward or the luck runs out. It is one of the most widely repeated pieces of decorating folklore in Britain.
It is also, as far as anyone can establish, not something the source traditions actually say. What they do say is more interesting, so here is an honest untangling.
Where the trunk up rule comes from
The claim is that a raised trunk showers good fortune while a lowered trunk lets it drain away. You will find it stated as ancient wisdom on a great many websites.
What is difficult to find is grounding for it in Hindu, Buddhist or Thai sources. It appears to be a modern Western folk belief, spread through the decorating and gift trade and reinforced by repetition online.
There is a related and more plausible reading in feng shui, where a raised trunk is sometimes associated with welcoming energy. Even there it is a preference rather than a rule, and feng shui is a Chinese tradition rather than an Indian one, which matters given where most elephant imagery originates.
What the Hindu tradition actually holds
The central figure is Ganesha, the elephant headed deity, remover of obstacles and patron of beginnings. He is invoked at the start of ventures and journeys, which is why he appears so often in homes and businesses.
The iconography that carries meaning is not trunk elevation but what Ganesha holds and how he is posed: the broken tusk, the noose, the goad, the bowl of sweets, the mouse that accompanies him. Trunk direction is discussed in some temple traditions, where a left curving trunk is the more common form and considered suitable for household worship, while right curving images are treated as requiring more rigorous ritual observance. Note that this concerns left and right rather than up and down.

Elephants in Buddhist tradition
Different again, and unrelated to fortune in the decorative sense.
A white elephant appears in the account of the Buddha's birth, where Queen Maya is said to have dreamt of one entering her side. Elephants also appear in Buddhist teaching as images of the mind: the untrained mind as a wild elephant, the trained mind as one that is steady and controllable, a recurring metaphor in meditation instruction.
Here the elephant stands for strength, patience and the disciplined mind rather than for luck.
The Thai and Southeast Asian view
In Thailand the elephant is a national symbol with a long royal association, and white elephants specifically were royal property, their possession tied to the prestige of a king.
That association gives English the phrase white elephant, meaning a burdensome possession, from accounts of monarchs gifting sacred white elephants to courtiers who could then neither work them nor dispose of them while remaining obliged to maintain them at great expense.
So does the trunk matter
Honestly, choose the one you prefer. If a raised trunk pleases you, have it, and there is a reasonable feng shui reading behind it. If a lowered trunk suits the piece better, nothing in the major traditions suggests you are inviting misfortune.
What the traditions do consistently care about, as with most religious imagery, is that the object is treated respectfully rather than casually.
Placement conventions that do have grounding
A few things recur and are worth following if you want to be thoughtful. Ganesha is traditionally placed near an entrance facing inward, since he is the remover of obstacles at thresholds. Raised rather than on the floor, as with most religious imagery. And kept clean, which in a British house mostly means dusted.
Pairs flanking a doorway is a common convention in several Asian traditions, which works well with our wall mount elephant heads either side of a hallway.
Choosing a piece
Our carved elephants include the freestanding turquoise and gold and white and gold figures, and wall mount heads in gold and grey, gold and turquoise and gold and whitewash.
Choose on carving, finish and how it suits the space, which is the honest basis for the decision and the one you would use for any other object in your home.
Questions people ask
Should an elephant ornament have its trunk up or down?
Either. The trunk up rule appears to be a modern Western folk belief rather than something the Hindu, Buddhist or Thai traditions hold. A feng shui reading favours a raised trunk, but as a preference rather than a rule.
What does the elephant mean in Hinduism?
Ganesha, the elephant headed deity, is the remover of obstacles and patron of beginnings. The meaningful iconography concerns what he holds and his pose, and where trunk direction is discussed it concerns left and right rather than up and down.
What do elephants mean in Buddhism?
Strength, patience and the disciplined mind. A white elephant appears in the account of the Buddha's conception, and the untrained mind is likened to a wild elephant in meditation teaching.
Where does the phrase white elephant come from?
From Southeast Asian royal tradition, where sacred white elephants were royal property. Monarchs are said to have gifted them to courtiers who could neither work nor dispose of them while being obliged to maintain them at ruinous cost.
Where should an elephant ornament be placed?
Near an entrance facing inward is the traditional placement for Ganesha, raised rather than on the floor and kept clean. Pairs flanking a doorway is a common convention.